Properties

Base field \(\Q(\sqrt{-1}) \)
Weight 2
Level norm 377
Level \( \left(11 i - 16\right) \)
Label 2.0.4.1-377.4-a2
Dimension 2
CM not determined
Base-change no
Sign not determined
Analytic rank not determined

Related objects

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Base Field: \(\Q(\sqrt{-1}) \)

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

Form

Weight 2
Level 377.4 = \( \left(11 i - 16\right) \)
Label 2.0.4.1-377.4-a2
Dimension: 2
CM: not determined
Base change: no
Newspace:2.0.4.1-377.4 (dimension 3)
Sign of functional equation: not determined
Analytic rank: not determined
L-ratio: not determined

Hecke eigenvalues

The Hecke eigenfield is \(\Q(z)\) where $z$ is a root of the defining polynomial: \( x^{2} - 2 \).

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( i + 1 \)) \( -z \)
\( 5 \) 5.1 = (\( -i - 2 \)) \( -1 \)
\( 5 \) 5.2 = (\( 2 i + 1 \)) \( 2 z \)
\( 9 \) 9.1 = (\( 3 \)) \( 2 z + 2 \)
\( 13 \) 13.1 = (\( -3 i - 2 \)) \( 2 z - 1 \)
\( 13 \) 13.2 = (\( 2 i + 3 \)) not known
\( 17 \) 17.1 = (\( i + 4 \)) \( 2 z + 3 \)
\( 17 \) 17.2 = (\( i - 4 \)) \( 4 \)
\( 29 \) 29.1 = (\( -2 i + 5 \)) \( 2 z + 1 \)
\( 29 \) 29.2 = (\( 2 i + 5 \)) not known
\( 37 \) 37.1 = (\( i + 6 \)) \( -4 z + 5 \)
\( 37 \) 37.2 = (\( i - 6 \)) \( -2 z - 5 \)
\( 41 \) 41.1 = (\( -5 i - 4 \)) \( 2 z + 1 \)
\( 41 \) 41.2 = (\( 4 i + 5 \)) \( -4 z + 5 \)
\( 49 \) 49.1 = (\( 7 \)) \( 2 z \)

Atkin-Lehner eigenvalues

Not known