Properties

Base field \(\Q(\sqrt{-7}) \)
Weight 2
Level norm 1444
Level \( \left(38\right) \)
Label 2.0.7.1-1444.2-b
Dimension 1
CM no
Base-change yes
Sign +1
Analytic rank \(0\)

Related objects

Learn more about

Base Field: \(\Q(\sqrt{-7}) \)

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

Form

Weight 2
Level 1444.2 = \( \left(38\right) \)
Label 2.0.7.1-1444.2-b
Dimension: 1
CM: no
Base change: yes 38.2.a.b , 1862.2.a.f
Newspace:2.0.7.1-1444.2 (dimension 2)
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 = (\( a \)) \( 1 \)
\( 2 \) 2.2 = (\( -a + 1 \)) \( 1 \)
\( 7 \) 7.1 = (\( -2 a + 1 \)) \( 3 \)
\( 9 \) 9.1 = (\( 3 \)) \( -5 \)
\( 11 \) 11.1 = (\( -2 a + 3 \)) \( 2 \)
\( 11 \) 11.2 = (\( 2 a + 1 \)) \( 2 \)
\( 23 \) 23.1 = (\( -2 a + 5 \)) \( -1 \)
\( 23 \) 23.2 = (\( 2 a + 3 \)) \( -1 \)
\( 25 \) 25.1 = (\( 5 \)) \( 6 \)
\( 29 \) 29.1 = (\( -4 a + 1 \)) \( -5 \)
\( 29 \) 29.2 = (\( 4 a - 3 \)) \( -5 \)
\( 37 \) 37.1 = (\( -4 a + 5 \)) \( -2 \)
\( 37 \) 37.2 = (\( 4 a + 1 \)) \( -2 \)
\( 43 \) 43.1 = (\( -2 a + 7 \)) \( 4 \)
\( 43 \) 43.2 = (\( 2 a + 5 \)) \( 4 \)
\( 53 \) 53.1 = (\( -4 a - 3 \)) \( -1 \)
\( 53 \) 53.2 = (\( 4 a - 7 \)) \( -1 \)
\( 67 \) 67.1 = (\( -6 a + 1 \)) \( 3 \)
\( 67 \) 67.2 = (\( 6 a - 5 \)) \( 3 \)
\( 71 \) 71.1 = (\( -2 a + 9 \)) \( 2 \)
\( 71 \) 71.2 = (\( 2 a + 7 \)) \( 2 \)
\( 79 \) 79.1 = (\( -6 a + 7 \)) \( -10 \)
\( 79 \) 79.2 = (\( 6 a + 1 \)) \( -10 \)
\( 107 \) 107.1 = (\( -2 a + 11 \)) \( -7 \)
\( 107 \) 107.2 = (\( 2 a + 9 \)) \( -7 \)
\( 109 \) 109.1 = (\( -4 a - 7 \)) \( -15 \)
\( 109 \) 109.2 = (\( 4 a - 11 \)) \( -15 \)
\( 113 \) 113.1 = (\( -8 a + 3 \)) \( 14 \)
\( 113 \) 113.2 = (\( -8 a + 5 \)) \( 14 \)
\( 127 \) 127.1 = (\( -6 a - 5 \)) \( 18 \)
\( 127 \) 127.2 = (\( 6 a - 11 \)) \( 18 \)
\( 137 \) 137.1 = (\( -8 a + 9 \)) \( -17 \)
\( 137 \) 137.2 = (\( 8 a + 1 \)) \( -17 \)
\( 149 \) 149.1 = (\( -4 a + 13 \)) \( 0 \)
\( 149 \) 149.2 = (\( 4 a + 9 \)) \( 0 \)
\( 151 \) 151.1 = (\( -2 a + 13 \)) \( 2 \)
\( 151 \) 151.2 = (\( 2 a + 11 \)) \( 2 \)
\( 163 \) 163.1 = (\( -6 a + 13 \)) \( -16 \)
\( 163 \) 163.2 = (\( 6 a + 7 \)) \( -16 \)
\( 169 \) 169.1 = (\( 13 \)) \( -25 \)
\( 179 \) 179.1 = (\( 10 a - 7 \)) \( 0 \)
\( 179 \) 179.2 = (\( 10 a - 3 \)) \( 0 \)
\( 191 \) 191.1 = (\( -10 a + 1 \)) \( 7 \)
\( 191 \) 191.2 = (\( 10 a - 9 \)) \( 7 \)
\( 193 \) 193.1 = (\( -8 a - 5 \)) \( -6 \)
\( 193 \) 193.2 = (\( -8 a + 13 \)) \( -6 \)
\( 197 \) 197.1 = (\( -4 a - 11 \)) \( 8 \)
\( 197 \) 197.2 = (\( 4 a - 15 \)) \( 8 \)
\( 211 \) 211.1 = (\( -10 a + 11 \)) \( 27 \)
\( 211 \) 211.2 = (\( 10 a + 1 \)) \( 27 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( a \)) \( -1 \)
\( 2 \) 2.2 = (\( -a + 1 \)) \( -1 \)
\( 361 \) 361.1 = (\( 19 \)) \( -1 \)