Properties

Base field \(\Q(\sqrt{-2}) \)
Weight 2
Level norm 10082
Level \( \left(71 a\right) \)
Label 2.0.8.1-10082.1-e
Dimension 1
CM no
Base-change yes
Sign -1
Analytic rank odd

Related objects

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

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

Form

Weight 2
Level 10082.1 = \( \left(71 a\right) \)
Label 2.0.8.1-10082.1-e
Dimension: 1
CM: no
Base change: yes 4544.2.a.k , 142.2.a.e
Newspace:2.0.8.1-10082.1 (dimension 5)
Sign of functional equation: -1
Analytic rank: odd

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( 1 \)
\( 3 \) 3.1 = (\( -a - 1 \)) \( 1 \)
\( 3 \) 3.2 = (\( a - 1 \)) \( 1 \)
\( 11 \) 11.1 = (\( a + 3 \)) \( 0 \)
\( 11 \) 11.2 = (\( a - 3 \)) \( 0 \)
\( 17 \) 17.1 = (\( -2 a + 3 \)) \( 0 \)
\( 17 \) 17.2 = (\( 2 a + 3 \)) \( 0 \)
\( 19 \) 19.1 = (\( -3 a + 1 \)) \( -1 \)
\( 19 \) 19.2 = (\( 3 a + 1 \)) \( -1 \)
\( 25 \) 25.1 = (\( 5 \)) \( -10 \)
\( 41 \) 41.1 = (\( -4 a - 3 \)) \( 0 \)
\( 41 \) 41.2 = (\( 4 a - 3 \)) \( 0 \)
\( 43 \) 43.1 = (\( -3 a - 5 \)) \( -1 \)
\( 43 \) 43.2 = (\( 3 a - 5 \)) \( -1 \)
\( 49 \) 49.1 = (\( 7 \)) \( -13 \)
\( 59 \) 59.1 = (\( -5 a + 3 \)) \( 6 \)
\( 59 \) 59.2 = (\( -5 a - 3 \)) \( 6 \)
\( 67 \) 67.1 = (\( -3 a + 7 \)) \( 8 \)
\( 67 \) 67.2 = (\( 3 a + 7 \)) \( 8 \)
\( 73 \) 73.1 = (\( -6 a + 1 \)) \( -1 \)
\( 73 \) 73.2 = (\( 6 a + 1 \)) \( -1 \)
\( 83 \) 83.1 = (\( a + 9 \)) \( 12 \)
\( 83 \) 83.2 = (\( a - 9 \)) \( 12 \)
\( 89 \) 89.1 = (\( -2 a + 9 \)) \( -3 \)
\( 89 \) 89.2 = (\( 2 a + 9 \)) \( -3 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( -1 \)
\( 5041 \) 5041.1 = (\( 71 \)) \( -1 \)