Properties

Base field \(\Q(\sqrt{-1}) \)
Weight 2
Level norm 100
Level \( \left(10\right) \)
Label 2.0.4.1-100.2-a
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 100.2 = \( \left(10\right) \)
Label 2.0.4.1-100.2-a
Dimension: 1
CM: no
Base change: yes 80.2.1.b , 20.2.1.a
Newspace:2.0.4.1-100.2 (dimension 1)
Sign of functional equation: +1
Analytic rank: \(0\)
L-ratio: 1/2

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( i + 1 \)) \( 0 \)
\( 5 \) 5.1 = (\( -i - 2 \)) \( -1 \)
\( 5 \) 5.2 = (\( 2 i + 1 \)) \( -1 \)
\( 9 \) 9.1 = (\( 3 \)) \( -2 \)
\( 13 \) 13.1 = (\( -3 i - 2 \)) \( 2 \)
\( 13 \) 13.2 = (\( 2 i + 3 \)) \( 2 \)
\( 17 \) 17.1 = (\( i + 4 \)) \( -6 \)
\( 17 \) 17.2 = (\( i - 4 \)) \( -6 \)
\( 29 \) 29.1 = (\( -2 i + 5 \)) \( 6 \)
\( 29 \) 29.2 = (\( 2 i + 5 \)) \( 6 \)
\( 37 \) 37.1 = (\( i + 6 \)) \( 2 \)
\( 37 \) 37.2 = (\( i - 6 \)) \( 2 \)
\( 41 \) 41.1 = (\( -5 i - 4 \)) \( 6 \)
\( 41 \) 41.2 = (\( 4 i + 5 \)) \( 6 \)
\( 49 \) 49.1 = (\( 7 \)) \( -10 \)
\( 53 \) 53.1 = (\( -2 i + 7 \)) \( -6 \)
\( 53 \) 53.2 = (\( 2 i + 7 \)) \( -6 \)
\( 61 \) 61.1 = (\( -6 i - 5 \)) \( 2 \)
\( 61 \) 61.2 = (\( 5 i + 6 \)) \( 2 \)
\( 73 \) 73.1 = (\( -3 i - 8 \)) \( 2 \)
\( 73 \) 73.2 = (\( 3 i - 8 \)) \( 2 \)
\( 89 \) 89.1 = (\( -5 i + 8 \)) \( -6 \)
\( 89 \) 89.2 = (\( -8 i + 5 \)) \( -6 \)
\( 97 \) 97.1 = (\( -4 i + 9 \)) \( 2 \)
\( 97 \) 97.2 = (\( 4 i + 9 \)) \( 2 \)
\( 101 \) 101.1 = (\( i + 10 \)) \( 6 \)
\( 101 \) 101.2 = (\( i - 10 \)) \( 6 \)
\( 109 \) 109.1 = (\( -3 i + 10 \)) \( 2 \)
\( 109 \) 109.2 = (\( 3 i + 10 \)) \( 2 \)
\( 113 \) 113.1 = (\( -8 i - 7 \)) \( -6 \)
\( 113 \) 113.2 = (\( 7 i + 8 \)) \( -6 \)
\( 121 \) 121.1 = (\( 11 \)) \( -22 \)
\( 137 \) 137.1 = (\( -4 i - 11 \)) \( 18 \)
\( 137 \) 137.2 = (\( 4 i - 11 \)) \( 18 \)
\( 149 \) 149.1 = (\( 10 i - 7 \)) \( -6 \)
\( 149 \) 149.2 = (\( 7 i - 10 \)) \( -6 \)
\( 157 \) 157.1 = (\( -6 i - 11 \)) \( -22 \)
\( 157 \) 157.2 = (\( 6 i - 11 \)) \( -22 \)
\( 173 \) 173.1 = (\( -2 i + 13 \)) \( -6 \)
\( 173 \) 173.2 = (\( 2 i + 13 \)) \( -6 \)
\( 181 \) 181.1 = (\( -10 i - 9 \)) \( -10 \)
\( 181 \) 181.2 = (\( 9 i + 10 \)) \( -10 \)
\( 193 \) 193.1 = (\( 7 i - 12 \)) \( 26 \)
\( 193 \) 193.2 = (\( 7 i + 12 \)) \( 26 \)
\( 197 \) 197.1 = (\( i + 14 \)) \( 18 \)
\( 197 \) 197.2 = (\( i - 14 \)) \( 18 \)
\( 229 \) 229.1 = (\( -2 i + 15 \)) \( 14 \)
\( 229 \) 229.2 = (\( 2 i + 15 \)) \( 14 \)
\( 233 \) 233.1 = (\( -8 i - 13 \)) \( -6 \)
\( 233 \) 233.2 = (\( -8 i + 13 \)) \( -6 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( i + 1 \)) \( -1 \)
\( 5 \) 5.1 = (\( -i - 2 \)) \( 1 \)
\( 5 \) 5.2 = (\( 2 i + 1 \)) \( 1 \)