Properties

Label 2.0.3.1-99372.5-g
Base field \(\Q(\sqrt{-3}) \)
Weight $2$
Level norm $99372$
Level \( \left(-364 a + 182\right) \)
Dimension $1$
CM no
Base change yes
Sign $-1$
Analytic rank odd

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Base field: \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 1\); class number \(1\).

Form

Weight: 2
Level: 99372.5 = \( \left(-364 a + 182\right) \)
Level norm: 99372
Dimension: 1
CM: no
Base change: yes 546.2.a.c , 1638.2.a.o
Newspace:2.0.3.1-99372.5 (dimension 23)
Sign of functional equation: $-1$
Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 3 \) 3.1 = \( \left(-2 a + 1\right) \) \( -1 \)
\( 4 \) 4.1 = \( \left(2\right) \) \( -1 \)
\( 7 \) 7.1 = \( \left(-3 a + 1\right) \) \( 1 \)
\( 7 \) 7.2 = \( \left(3 a - 2\right) \) \( 1 \)
\( 13 \) 13.1 = \( \left(-4 a + 1\right) \) \( 1 \)
\( 13 \) 13.2 = \( \left(4 a - 3\right) \) \( 1 \)

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 19 \) 19.1 = \( \left(-5 a + 3\right) \) \( 1 \)
\( 19 \) 19.2 = \( \left(-5 a + 2\right) \) \( 1 \)
\( 25 \) 25.1 = \( \left(5\right) \) \( -9 \)
\( 31 \) 31.1 = \( \left(-6 a + 1\right) \) \( 4 \)
\( 31 \) 31.2 = \( \left(6 a - 5\right) \) \( 4 \)
\( 37 \) 37.1 = \( \left(-7 a + 4\right) \) \( -5 \)
\( 37 \) 37.2 = \( \left(-7 a + 3\right) \) \( -5 \)
\( 43 \) 43.1 = \( \left(-7 a + 1\right) \) \( -1 \)
\( 43 \) 43.2 = \( \left(7 a - 6\right) \) \( -1 \)
\( 61 \) 61.1 = \( \left(-9 a + 5\right) \) \( 13 \)
\( 61 \) 61.2 = \( \left(-9 a + 4\right) \) \( 13 \)
\( 67 \) 67.1 = \( \left(9 a - 7\right) \) \( -10 \)
\( 67 \) 67.2 = \( \left(9 a - 2\right) \) \( -10 \)
\( 73 \) 73.1 = \( \left(-9 a + 1\right) \) \( -15 \)
\( 73 \) 73.2 = \( \left(9 a - 8\right) \) \( -15 \)
\( 79 \) 79.1 = \( \left(10 a - 7\right) \) \( 6 \)
\( 79 \) 79.2 = \( \left(10 a - 3\right) \) \( 6 \)
\( 97 \) 97.1 = \( \left(-11 a + 3\right) \) \( -2 \)
\( 97 \) 97.2 = \( \left(-11 a + 8\right) \) \( -2 \)
\( 103 \) 103.1 = \( \left(11 a - 9\right) \) \( 1 \)
Display number of eigenvalues