Properties

Base field \(\Q(\sqrt{-7}) \)
Weight 2
Level norm 16384
Level \( \left(128\right) \)
Label 2.0.7.1-16384.8-b
Dimension 1
CM no
Base-change yes
Sign -1
Analytic rank odd

Related objects

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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 16384.8 = \( \left(128\right) \)
Label 2.0.7.1-16384.8-b
Dimension: 1
CM: no
Base change: yes 128.2.a.a , 6272.2.a.h
Newspace:2.0.7.1-16384.8 (dimension 32)
Sign of functional equation: -1
Analytic rank: odd

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( 0 \)
\( 2 \) 2.2 = (\( -a + 1 \)) \( 0 \)
\( 7 \) 7.1 = (\( -2 a + 1 \)) \( -4 \)
\( 9 \) 9.1 = (\( 3 \)) \( -2 \)
\( 11 \) 11.1 = (\( -2 a + 3 \)) \( 2 \)
\( 11 \) 11.2 = (\( 2 a + 1 \)) \( 2 \)
\( 23 \) 23.1 = (\( -2 a + 5 \)) \( 4 \)
\( 23 \) 23.2 = (\( 2 a + 3 \)) \( 4 \)
\( 25 \) 25.1 = (\( 5 \)) \( -6 \)
\( 29 \) 29.1 = (\( -4 a + 1 \)) \( 6 \)
\( 29 \) 29.2 = (\( 4 a - 3 \)) \( 6 \)
\( 37 \) 37.1 = (\( -4 a + 5 \)) \( -10 \)
\( 37 \) 37.2 = (\( 4 a + 1 \)) \( -10 \)
\( 43 \) 43.1 = (\( -2 a + 7 \)) \( -6 \)
\( 43 \) 43.2 = (\( 2 a + 5 \)) \( -6 \)
\( 53 \) 53.1 = (\( -4 a - 3 \)) \( 6 \)
\( 53 \) 53.2 = (\( 4 a - 7 \)) \( 6 \)
\( 67 \) 67.1 = (\( -6 a + 1 \)) \( -10 \)
\( 67 \) 67.2 = (\( 6 a - 5 \)) \( -10 \)
\( 71 \) 71.1 = (\( -2 a + 9 \)) \( 12 \)
\( 71 \) 71.2 = (\( 2 a + 7 \)) \( 12 \)
\( 79 \) 79.1 = (\( -6 a + 7 \)) \( -8 \)
\( 79 \) 79.2 = (\( 6 a + 1 \)) \( -8 \)
\( 107 \) 107.1 = (\( -2 a + 11 \)) \( 2 \)
\( 107 \) 107.2 = (\( 2 a + 9 \)) \( 2 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( 1 \)
\( 2 \) 2.2 = (\( -a + 1 \)) \( 1 \)