Properties

Label 2.0.15.1-48.5-b
Base field \(\Q(\sqrt{-15}) \)
Weight $2$
Level norm $48$
Level \( \left(48, a + 19\right) \)
Dimension $1$
CM no
Base change no
Sign $+1$
Analytic rank \(0\)

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Base field: \(\Q(\sqrt{-15}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 4\); class number \(2\).

Form

Weight: 2
Level: 48.5 = \( \left(48, a + 19\right) \)
Level norm: 48
Dimension: 1
CM: no
Base change: no
Newspace:2.0.15.1-48.5 (dimension 2)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 1/2

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.2 = \( \left(2, a + 1\right) \) \( 1 \)
\( 3 \) 3.1 = \( \left(3, a + 1\right) \) \( -1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 2 \) 2.1 = \( \left(2, a\right) \) \( 1 \)
\( 5 \) 5.1 = \( \left(5, a + 2\right) \) \( 2 \)
\( 17 \) 17.1 = \( \left(17, a + 5\right) \) \( 6 \)
\( 17 \) 17.2 = \( \left(17, a + 11\right) \) \( -2 \)
\( 19 \) 19.1 = \( \left(-2 a + 3\right) \) \( -4 \)
\( 19 \) 19.2 = \( \left(2 a + 1\right) \) \( -4 \)
\( 23 \) 23.1 = \( \left(23, a + 6\right) \) \( 0 \)
\( 23 \) 23.2 = \( \left(23, a + 16\right) \) \( 0 \)
\( 31 \) 31.1 = \( \left(-2 a + 5\right) \) \( 0 \)
\( 31 \) 31.2 = \( \left(2 a + 3\right) \) \( -8 \)
\( 47 \) 47.1 = \( \left(47, a + 9\right) \) \( 8 \)
\( 47 \) 47.2 = \( \left(47, a + 37\right) \) \( 8 \)
\( 49 \) 49.1 = \( \left(7\right) \) \( 2 \)
\( 53 \) 53.1 = \( \left(53, a + 20\right) \) \( -6 \)
\( 53 \) 53.2 = \( \left(53, a + 32\right) \) \( -6 \)
\( 61 \) 61.1 = \( \left(-4 a + 1\right) \) \( -2 \)
\( 61 \) 61.2 = \( \left(4 a - 3\right) \) \( -2 \)
\( 79 \) 79.1 = \( \left(-2 a + 9\right) \) \( 0 \)
\( 79 \) 79.2 = \( \left(2 a + 7\right) \) \( -8 \)
\( 83 \) 83.1 = \( \left(83, a + 31\right) \) \( 4 \)
Display number of eigenvalues