Properties

Label 2.0.31.1-100.2-c
Base field \(\Q(\sqrt{-31}) \)
Weight $2$
Level norm $100$
Level \( \left(20, 5 a\right) \)
Dimension $1$
CM no
Base change no
Sign $+1$
Analytic rank \(0\)

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Base field: \(\Q(\sqrt{-31}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 8\); class number \(3\).

Form

Weight: 2
Level: 100.2 = \( \left(20, 5 a\right) \)
Level norm: 100
Dimension: 1
CM: no
Base change: no
Newspace:2.0.31.1-100.2 (dimension 5)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 1

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = \( \left(2, a\right) \) \( -1 \)
\( 5 \) 5.1 = \( \left(5, a + 1\right) \) \( 1 \)
\( 5 \) 5.2 = \( \left(5, a + 3\right) \) \( 1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 2 \) 2.2 = \( \left(2, a + 1\right) \) \( 1 \)
\( 7 \) 7.1 = \( \left(7, a + 2\right) \) \( -2 \)
\( 7 \) 7.2 = \( \left(7, a + 4\right) \) \( -4 \)
\( 9 \) 9.1 = \( \left(3\right) \) \( 2 \)
\( 19 \) 19.1 = \( \left(19, a + 5\right) \) \( -6 \)
\( 19 \) 19.2 = \( \left(19, a + 13\right) \) \( 6 \)
\( 31 \) 31.1 = \( \left(-2 a + 1\right) \) \( -2 \)
\( 41 \) 41.1 = \( \left(41, a + 12\right) \) \( 10 \)
\( 41 \) 41.2 = \( \left(41, a + 28\right) \) \( -10 \)
\( 47 \) 47.1 = \( \left(-2 a + 5\right) \) \( 12 \)
\( 47 \) 47.2 = \( \left(2 a + 3\right) \) \( -2 \)
\( 59 \) 59.1 = \( \left(59, a + 10\right) \) \( 8 \)
\( 59 \) 59.2 = \( \left(59, a + 48\right) \) \( 0 \)
\( 67 \) 67.1 = \( \left(-2 a + 7\right) \) \( -6 \)
\( 67 \) 67.2 = \( \left(2 a + 5\right) \) \( 4 \)
\( 71 \) 71.1 = \( \left(71, a + 26\right) \) \( 10 \)
\( 71 \) 71.2 = \( \left(71, a + 44\right) \) \( 10 \)
\( 97 \) 97.1 = \( \left(97, a + 19\right) \) \( -14 \)
\( 97 \) 97.2 = \( \left(97, a + 77\right) \) \( -14 \)
\( 101 \) 101.1 = \( \left(101, a + 37\right) \) \( 10 \)
Display number of eigenvalues