Properties

Label 2.0.163.1-729.1-a
Base field \(\Q(\sqrt{-163}) \)
Weight $2$
Level norm $729$
Level \( \left(27\right) \)
Dimension $1$
CM $-3$
Base change yes
Sign $+1$
Analytic rank \(0\)

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Base field: \(\Q(\sqrt{-163}) \)

Generator \(a\), with minimal polynomial \(x^2 - x + 41\); class number \(1\).

Form

Weight: 2
Level: 729.1 = \( \left(27\right) \)
Level norm: 729
Dimension: 1
CM: $-3$
Base change: yes 27.2.a.a
Newspace:2.0.163.1-729.1 (dimension 109)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 1

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 9 \) 9.1 = \( \left(3\right) \) \( -1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 4 \) 4.1 = \( \left(2\right) \) \( -4 \)
\( 25 \) 25.1 = \( \left(5\right) \) \( -10 \)
\( 41 \) 41.1 = \( \left(-a\right) \) \( 0 \)
\( 41 \) 41.2 = \( \left(a - 1\right) \) \( 0 \)
\( 43 \) 43.1 = \( \left(a + 1\right) \) \( 8 \)
\( 43 \) 43.2 = \( \left(a - 2\right) \) \( 8 \)
\( 47 \) 47.1 = \( \left(a + 2\right) \) \( 0 \)
\( 47 \) 47.2 = \( \left(a - 3\right) \) \( 0 \)
\( 49 \) 49.1 = \( \left(7\right) \) \( -13 \)
\( 53 \) 53.1 = \( \left(a + 3\right) \) \( 0 \)
\( 53 \) 53.2 = \( \left(a - 4\right) \) \( 0 \)
\( 61 \) 61.1 = \( \left(a + 4\right) \) \( -1 \)
\( 61 \) 61.2 = \( \left(a - 5\right) \) \( -1 \)
\( 71 \) 71.1 = \( \left(a + 5\right) \) \( 0 \)
\( 71 \) 71.2 = \( \left(a - 6\right) \) \( 0 \)
\( 83 \) 83.1 = \( \left(a + 6\right) \) \( 0 \)
\( 83 \) 83.2 = \( \left(a - 7\right) \) \( 0 \)
\( 97 \) 97.1 = \( \left(a + 7\right) \) \( -19 \)
\( 97 \) 97.2 = \( \left(a - 8\right) \) \( -19 \)
\( 113 \) 113.1 = \( \left(a + 8\right) \) \( 0 \)
Display number of eigenvalues