Properties

Label 2.0.163.1-256.1-a
Base field \(\Q(\sqrt{-163}) \)
Weight $2$
Level norm $256$
Level \( \left(16\right) \)
Dimension $1$
CM no
Base change no
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: 256.1 = \( \left(16\right) \)
Level norm: 256
Dimension: 1
CM: no
Base change: no, but is a twist of the base change of a form over \(\mathbb{Q}\)
Newspace:2.0.163.1-256.1 (dimension 78)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 4

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 4 \) 4.1 = (\( 2 \)) \( -1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 9 \) 9.1 = (\( 3 \)) \( -6 \)
\( 25 \) 25.1 = (\( 5 \)) \( 1 \)
\( 41 \) 41.1 = (\( -a \)) \( 5 \)
\( 41 \) 41.2 = (\( a - 1 \)) \( 5 \)
\( 43 \) 43.1 = (\( a + 1 \)) \( -9 \)
\( 43 \) 43.2 = (\( a - 2 \)) \( 9 \)
\( 47 \) 47.1 = (\( a + 2 \)) \( 8 \)
\( 47 \) 47.2 = (\( a - 3 \)) \( -8 \)
\( 49 \) 49.1 = (\( 7 \)) \( -5 \)
\( 53 \) 53.1 = (\( a + 3 \)) \( 4 \)
\( 53 \) 53.2 = (\( a - 4 \)) \( 4 \)
\( 61 \) 61.1 = (\( a + 4 \)) \( 6 \)
\( 61 \) 61.2 = (\( a - 5 \)) \( 6 \)
\( 71 \) 71.1 = (\( a + 5 \)) \( 8 \)
\( 71 \) 71.2 = (\( a - 6 \)) \( -8 \)
\( 83 \) 83.1 = (\( a + 6 \)) \( -11 \)
\( 83 \) 83.2 = (\( a - 7 \)) \( 11 \)
\( 97 \) 97.1 = (\( a + 7 \)) \( -15 \)
\( 97 \) 97.2 = (\( a - 8 \)) \( -15 \)
\( 113 \) 113.1 = (\( a + 8 \)) \( -2 \)
Display number of eigenvalues