Properties

Base field \(\Q(\sqrt{-2}) \)
Weight 2
Level norm 15138
Level \( \left(87 a\right) \)
Label 2.0.8.1-15138.2-g
Dimension 1
CM no
Base-change yes
Sign -1
Analytic rank odd

Related objects

Learn more about

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

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

Form

Weight 2
Level 15138.2 = \( \left(87 a\right) \)
Label 2.0.8.1-15138.2-g
Dimension: 1
CM: no
Base change: yes 5568.2.a.bc , 174.2.a.e
Newspace:2.0.8.1-15138.2 (dimension 7)
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 = (\( a + 3 \)) \( -2 \)
\( 11 \) 11.2 = (\( a - 3 \)) \( -2 \)
\( 17 \) 17.1 = (\( -2 a + 3 \)) \( -3 \)
\( 17 \) 17.2 = (\( 2 a + 3 \)) \( -3 \)
\( 19 \) 19.1 = (\( -3 a + 1 \)) \( -1 \)
\( 19 \) 19.2 = (\( 3 a + 1 \)) \( -1 \)
\( 25 \) 25.1 = (\( 5 \)) \( -9 \)
\( 41 \) 41.1 = (\( -4 a - 3 \)) \( -7 \)
\( 41 \) 41.2 = (\( 4 a - 3 \)) \( -7 \)
\( 43 \) 43.1 = (\( -3 a - 5 \)) \( 9 \)
\( 43 \) 43.2 = (\( 3 a - 5 \)) \( 9 \)
\( 49 \) 49.1 = (\( 7 \)) \( -13 \)
\( 59 \) 59.1 = (\( -5 a + 3 \)) \( -3 \)
\( 59 \) 59.2 = (\( -5 a - 3 \)) \( -3 \)
\( 67 \) 67.1 = (\( -3 a + 7 \)) \( 12 \)
\( 67 \) 67.2 = (\( 3 a + 7 \)) \( 12 \)
\( 73 \) 73.1 = (\( -6 a + 1 \)) \( -10 \)
\( 73 \) 73.2 = (\( 6 a + 1 \)) \( -10 \)
\( 83 \) 83.1 = (\( a + 9 \)) \( 0 \)
\( 83 \) 83.2 = (\( a - 9 \)) \( 0 \)
\( 89 \) 89.1 = (\( -2 a + 9 \)) \( 6 \)
\( 89 \) 89.2 = (\( 2 a + 9 \)) \( 6 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( -1 \)
\( 3 \) 3.1 = (\( -a - 1 \)) \( -1 \)
\( 3 \) 3.2 = (\( a - 1 \)) \( -1 \)
\( 841 \) 841.1 = (\( 29 \)) \( -1 \)