Properties

Label 2.0.7.1-218.2-a
Base field \(\Q(\sqrt{-7}) \)
Weight $2$
Level norm $218$
Level \( \left(7 a + 8\right) \)
Dimension $1$
CM no
Base change no
Sign $+1$
Analytic rank \(0\)

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Base field: \(\Q(\sqrt{-7}) \)

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

Form

Weight: 2
Level: 218.2 = \( \left(7 a + 8\right) \)
Level norm: 218
Dimension: 1
CM: no
Base change: no
Newspace:2.0.7.1-218.2 (dimension 1)
Sign of functional equation: $+1$
Analytic rank: \(0\)
L-ratio: 1

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( 1 \)
\( 109 \) 109.2 = (\( 4 a - 11 \)) \( -1 \)

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 1000 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 = (\( -a + 1 \)) \( 0 \)
\( 7 \) 7.1 = (\( -2 a + 1 \)) \( -1 \)
\( 9 \) 9.1 = (\( 3 \)) \( 4 \)
\( 11 \) 11.1 = (\( -2 a + 3 \)) \( 0 \)
\( 11 \) 11.2 = (\( 2 a + 1 \)) \( 0 \)
\( 23 \) 23.1 = (\( -2 a + 5 \)) \( 6 \)
\( 23 \) 23.2 = (\( 2 a + 3 \)) \( -3 \)
\( 25 \) 25.1 = (\( 5 \)) \( 8 \)
\( 29 \) 29.1 = (\( -4 a + 1 \)) \( 0 \)
\( 29 \) 29.2 = (\( 4 a - 3 \)) \( 3 \)
\( 37 \) 37.1 = (\( -4 a + 5 \)) \( -7 \)
\( 37 \) 37.2 = (\( 4 a + 1 \)) \( 11 \)
\( 43 \) 43.1 = (\( -2 a + 7 \)) \( -1 \)
\( 43 \) 43.2 = (\( 2 a + 5 \)) \( -10 \)
\( 53 \) 53.1 = (\( -4 a - 3 \)) \( 6 \)
\( 53 \) 53.2 = (\( 4 a - 7 \)) \( 9 \)
\( 67 \) 67.1 = (\( -6 a + 1 \)) \( -4 \)
\( 67 \) 67.2 = (\( 6 a - 5 \)) \( 5 \)
\( 71 \) 71.1 = (\( -2 a + 9 \)) \( -12 \)
\( 71 \) 71.2 = (\( 2 a + 7 \)) \( 3 \)
\( 79 \) 79.1 = (\( -6 a + 7 \)) \( -10 \)
Display number of eigenvalues