Properties

Label 2.0.8.1-392.1-a
Base field \(\Q(\sqrt{-2}) \)
Weight $2$
Level norm $392$
Level \( \left(14 a\right) \)
Dimension $1$
CM no
Base change yes
Sign $-1$
Analytic rank odd

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Base field: \(\Q(\sqrt{-2}) \)

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

Form

Weight: 2
Level: 392.1 = \( \left(14 a\right) \)
Level norm: 392
Dimension: 1
CM: no
Base change: yes 56.2.a.a , 448.2.a.e
Newspace:2.0.8.1-392.1 (dimension 2)
Sign of functional equation: $-1$
Analytic rank: odd

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( -1 \)
\( 49 \) 49.1 = (\( 7 \)) \( -1 \)

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.

$N(\mathfrak{p})$ $\mathfrak{p}$ $a_{\mathfrak{p}}$
\( 3 \) 3.1 = (\( -a - 1 \)) \( 0 \)
\( 3 \) 3.2 = (\( a - 1 \)) \( 0 \)
\( 11 \) 11.1 = (\( a + 3 \)) \( -4 \)
\( 11 \) 11.2 = (\( a - 3 \)) \( -4 \)
\( 17 \) 17.1 = (\( -2 a + 3 \)) \( -6 \)
\( 17 \) 17.2 = (\( 2 a + 3 \)) \( -6 \)
\( 19 \) 19.1 = (\( -3 a + 1 \)) \( 8 \)
\( 19 \) 19.2 = (\( 3 a + 1 \)) \( 8 \)
\( 25 \) 25.1 = (\( 5 \)) \( -6 \)
\( 41 \) 41.1 = (\( -4 a - 3 \)) \( 2 \)
\( 41 \) 41.2 = (\( 4 a - 3 \)) \( 2 \)
\( 43 \) 43.1 = (\( -3 a - 5 \)) \( -4 \)
\( 43 \) 43.2 = (\( 3 a - 5 \)) \( -4 \)
\( 59 \) 59.1 = (\( -5 a + 3 \)) \( 0 \)
\( 59 \) 59.2 = (\( -5 a - 3 \)) \( 0 \)
\( 67 \) 67.1 = (\( -3 a + 7 \)) \( -4 \)
\( 67 \) 67.2 = (\( 3 a + 7 \)) \( -4 \)
\( 73 \) 73.1 = (\( -6 a + 1 \)) \( 10 \)
\( 73 \) 73.2 = (\( 6 a + 1 \)) \( 10 \)
\( 83 \) 83.1 = (\( a + 9 \)) \( 8 \)
Display number of eigenvalues