Properties

Base field \(\Q(\sqrt{-1}) \)
Weight 2
Level norm 16384
Level \( \left(128\right) \)
Label 2.0.4.1-16384.1-d
Dimension 1
CM no
Base-change yes
Sign +1
Analytic rank \(0\)

Related objects

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

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

Form

Weight 2
Level 16384.1 = \( \left(128\right) \)
Label 2.0.4.1-16384.1-d
Dimension: 1
CM: no
Base change: yes, of a form over \(\mathbb{Q}\) with coefficients in \(\mathbb{Q}(\sqrt{2})\)
Newspace:2.0.4.1-16384.1 (dimension 14)
Sign of functional equation: +1
Analytic rank: \(0\)
L-ratio: 1

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( i + 1 \)) \( 0 \)
\( 5 \) 5.1 = (\( -i - 2 \)) \( 2 \)
\( 5 \) 5.2 = (\( 2 i + 1 \)) \( 2 \)
\( 9 \) 9.1 = (\( 3 \)) \( -4 \)
\( 13 \) 13.1 = (\( -3 i - 2 \)) \( 6 \)
\( 13 \) 13.2 = (\( 2 i + 3 \)) \( 6 \)
\( 17 \) 17.1 = (\( i + 4 \)) \( 0 \)
\( 17 \) 17.2 = (\( i - 4 \)) \( 0 \)
\( 29 \) 29.1 = (\( -2 i + 5 \)) \( 2 \)
\( 29 \) 29.2 = (\( 2 i + 5 \)) \( 2 \)
\( 37 \) 37.1 = (\( i + 6 \)) \( 6 \)
\( 37 \) 37.2 = (\( i - 6 \)) \( 6 \)
\( 41 \) 41.1 = (\( -5 i - 4 \)) \( 6 \)
\( 41 \) 41.2 = (\( 4 i + 5 \)) \( 6 \)
\( 49 \) 49.1 = (\( 7 \)) \( -6 \)
\( 53 \) 53.1 = (\( -2 i + 7 \)) \( -2 \)
\( 53 \) 53.2 = (\( 2 i + 7 \)) \( -2 \)
\( 61 \) 61.1 = (\( -6 i - 5 \)) \( 6 \)
\( 61 \) 61.2 = (\( 5 i + 6 \)) \( 6 \)
\( 73 \) 73.1 = (\( -3 i - 8 \)) \( -12 \)
\( 73 \) 73.2 = (\( 3 i - 8 \)) \( -12 \)
\( 89 \) 89.1 = (\( -5 i + 8 \)) \( -12 \)
\( 89 \) 89.2 = (\( -8 i + 5 \)) \( -12 \)
\( 97 \) 97.1 = (\( -4 i + 9 \)) \( -8 \)
\( 97 \) 97.2 = (\( 4 i + 9 \)) \( -8 \)

Atkin-Lehner eigenvalues

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