Base field 4.4.18688.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[32, 4, -2w - 4]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
7 | $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ | $-2$ |
7 | $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ | $\phantom{-}2$ |
9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ | $-1$ |
9 | $[9, 3, w + 1]$ | $-5$ |
17 | $[17, 17, w + 3]$ | $\phantom{-}7$ |
17 | $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ | $-5$ |
31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ | $\phantom{-}2$ |
31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ | $-10$ |
41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ | $-9$ |
41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}7$ |
41 | $[41, 41, 2w + 3]$ | $\phantom{-}11$ |
41 | $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ | $-5$ |
47 | $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ | $\phantom{-}10$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ | $\phantom{-}6$ |
49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ | $\phantom{-}3$ |
73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ | $\phantom{-}7$ |
73 | $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ | $\phantom{-}3$ |
73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ | $\phantom{-}6$ |
103 | $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ | $-6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 2]$ | $1$ |