Properties

Label 2.0.24.1-98.2-b
Base field \(\Q(\sqrt{-6}) \)
Weight $2$
Level norm $98$
Level \( \left(14, 7 a\right) \)
Dimension $1$
CM no
Base change yes
Sign $+1$
Analytic rank \(0\)

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Base field: \(\Q(\sqrt{-6}) \)

Generator \(a\), with minimal polynomial \(x^2 + 6\); class number \(2\).

Form

Weight: 2
Level: 98.2 = \( \left(14, 7 a\right) \)
Level norm: 98
Dimension: 1
CM: no
Base change: yes 448.2.a.g , 126.2.a.b
Newspace:2.0.24.1-98.2 (dimension 2)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 3/2

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = \( \left(2, a\right) \) \( -1 \)
\( 7 \) 7.1 = \( \left(a + 1\right) \) \( -1 \)
\( 7 \) 7.2 = \( \left(a - 1\right) \) \( -1 \)

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 100 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 3 \) 3.1 = \( \left(3, a\right) \) \( 2 \)
\( 5 \) 5.1 = \( \left(5, a + 2\right) \) \( 0 \)
\( 5 \) 5.2 = \( \left(5, a + 3\right) \) \( 0 \)
\( 11 \) 11.1 = \( \left(11, a + 4\right) \) \( 0 \)
\( 11 \) 11.2 = \( \left(11, a + 7\right) \) \( 0 \)
\( 29 \) 29.1 = \( \left(29, a + 9\right) \) \( 6 \)
\( 29 \) 29.2 = \( \left(29, a + 20\right) \) \( 6 \)
\( 31 \) 31.1 = \( \left(a + 5\right) \) \( -4 \)
\( 31 \) 31.2 = \( \left(a - 5\right) \) \( -4 \)
\( 53 \) 53.1 = \( \left(53, a + 10\right) \) \( -6 \)
\( 53 \) 53.2 = \( \left(53, a + 43\right) \) \( -6 \)
\( 59 \) 59.1 = \( \left(59, a + 17\right) \) \( 6 \)
\( 59 \) 59.2 = \( \left(59, a + 42\right) \) \( 6 \)
\( 73 \) 73.1 = \( \left(-2 a + 7\right) \) \( 2 \)
\( 73 \) 73.2 = \( \left(2 a + 7\right) \) \( 2 \)
\( 79 \) 79.1 = \( \left(-3 a - 5\right) \) \( 8 \)
\( 79 \) 79.2 = \( \left(3 a - 5\right) \) \( 8 \)
\( 83 \) 83.1 = \( \left(83, a + 34\right) \) \( 6 \)
\( 83 \) 83.2 = \( \left(83, a + 49\right) \) \( 6 \)
\( 97 \) 97.1 = \( \left(-4 a + 1\right) \) \( -10 \)
Display number of eigenvalues