Defining parameters
| Level: | \( N \) | \(=\) | \( 550680 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 353 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 550680.a (trivial) |
| Character field: | \(\Q\) | ||
| Sturm bound: | \(237888\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(550680))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 118976 | 8448 | 110528 |
| Cusp forms | 118913 | 8448 | 110465 |
| Eisenstein series | 63 | 0 | 63 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
| \(2\) | \(3\) | \(5\) | \(13\) | \(353\) | Fricke | Dim |
|---|---|---|---|---|---|---|
| \(+\) | \(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(268\) |
| \(+\) | \(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(260\) |
| \(+\) | \(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(265\) |
| \(+\) | \(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(263\) |
| \(+\) | \(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(257\) |
| \(+\) | \(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(272\) |
| \(+\) | \(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(266\) |
| \(+\) | \(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(261\) |
| \(+\) | \(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(263\) |
| \(+\) | \(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(266\) |
| \(+\) | \(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(260\) |
| \(+\) | \(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(267\) |
| \(+\) | \(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(262\) |
| \(+\) | \(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(266\) |
| \(+\) | \(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(271\) |
| \(+\) | \(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(257\) |
| \(-\) | \(+\) | \(+\) | \(+\) | \(+\) | $-$ | \(274\) |
| \(-\) | \(+\) | \(+\) | \(+\) | \(-\) | $+$ | \(252\) |
| \(-\) | \(+\) | \(+\) | \(-\) | \(+\) | $+$ | \(249\) |
| \(-\) | \(+\) | \(+\) | \(-\) | \(-\) | $-$ | \(281\) |
| \(-\) | \(+\) | \(-\) | \(+\) | \(+\) | $+$ | \(258\) |
| \(-\) | \(+\) | \(-\) | \(+\) | \(-\) | $-$ | \(273\) |
| \(-\) | \(+\) | \(-\) | \(-\) | \(+\) | $-$ | \(275\) |
| \(-\) | \(+\) | \(-\) | \(-\) | \(-\) | $+$ | \(250\) |
| \(-\) | \(-\) | \(+\) | \(+\) | \(+\) | $+$ | \(264\) |
| \(-\) | \(-\) | \(+\) | \(+\) | \(-\) | $-$ | \(267\) |
| \(-\) | \(-\) | \(+\) | \(-\) | \(+\) | $-$ | \(269\) |
| \(-\) | \(-\) | \(+\) | \(-\) | \(-\) | $+$ | \(256\) |
| \(-\) | \(-\) | \(-\) | \(+\) | \(+\) | $-$ | \(268\) |
| \(-\) | \(-\) | \(-\) | \(+\) | \(-\) | $+$ | \(258\) |
| \(-\) | \(-\) | \(-\) | \(-\) | \(+\) | $+$ | \(255\) |
| \(-\) | \(-\) | \(-\) | \(-\) | \(-\) | $-$ | \(275\) |
| Plus space | \(+\) | \(4156\) | ||||
| Minus space | \(-\) | \(4292\) | ||||
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(550680))\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(550680))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(550680)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(353))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(706))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1059))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1412))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1765))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2118))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2824))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3530))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4236))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4589))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5295))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(7060))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(8472))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(9178))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(10590))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(13767))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(18356))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22945))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27534))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36712))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45890))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55068))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68835))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91780))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(137670))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275340))\)\(^{\oplus 2}\)