Properties

Label 2.0.23.1-52.1-a
Base field \(\Q(\sqrt{-23}) \)
Weight $2$
Level norm $52$
Level \( \left(52, a + 30\right) \)
Dimension $1$
CM no
Base change no
Sign $+1$
Analytic rank \(0\)

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Base field: \(\Q(\sqrt{-23}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 6\); class number \(3\).

Form

Weight: 2
Level: 52.1 = \( \left(52, a + 30\right) \)
Level norm: 52
Dimension: 1
CM: no
Base change: no
Newspace:2.0.23.1-52.1 (dimension 1)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 1/2

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = \( \left(2, a\right) \) \( -1 \)
\( 13 \) 13.1 = \( \left(13, a + 4\right) \) \( 1 \)

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 = \( \left(2, a + 1\right) \) \( 1 \)
\( 3 \) 3.1 = \( \left(3, a\right) \) \( 2 \)
\( 3 \) 3.2 = \( \left(3, a + 2\right) \) \( 2 \)
\( 13 \) 13.2 = \( \left(13, a + 8\right) \) \( 6 \)
\( 23 \) 23.1 = \( \left(-2 a + 1\right) \) \( -8 \)
\( 25 \) 25.1 = \( \left(5\right) \) \( -6 \)
\( 29 \) 29.1 = \( \left(29, a + 10\right) \) \( 2 \)
\( 29 \) 29.2 = \( \left(29, a + 18\right) \) \( 10 \)
\( 31 \) 31.1 = \( \left(31, a + 7\right) \) \( 0 \)
\( 31 \) 31.2 = \( \left(31, a + 23\right) \) \( 2 \)
\( 41 \) 41.1 = \( \left(41, a + 15\right) \) \( -6 \)
\( 41 \) 41.2 = \( \left(41, a + 25\right) \) \( -6 \)
\( 47 \) 47.1 = \( \left(47, a + 13\right) \) \( 4 \)
\( 47 \) 47.2 = \( \left(47, a + 33\right) \) \( -6 \)
\( 49 \) 49.1 = \( \left(7\right) \) \( 2 \)
\( 59 \) 59.1 = \( \left(-2 a + 7\right) \) \( -6 \)
\( 59 \) 59.2 = \( \left(2 a + 5\right) \) \( 0 \)
\( 71 \) 71.1 = \( \left(71, a + 20\right) \) \( 12 \)
\( 71 \) 71.2 = \( \left(71, a + 50\right) \) \( -2 \)
\( 73 \) 73.1 = \( \left(73, a + 29\right) \) \( 10 \)
Display number of eigenvalues