Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, w + 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $\phantom{-}3$ |
9 | $[9, 3, -w^{3} + 8w + 8]$ | $-6$ |
16 | $[16, 2, 2]$ | $\phantom{-}3$ |
19 | $[19, 19, w + 1]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{2} + 6]$ | $-5$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $\phantom{-}1$ |
19 | $[19, 19, -w + 2]$ | $-7$ |
25 | $[25, 5, 2w^{2} - 2w - 13]$ | $\phantom{-}2$ |
29 | $[29, 29, -w^{2} + 9]$ | $\phantom{-}9$ |
29 | $[29, 29, -w^{2} + 2w + 6]$ | $-2$ |
29 | $[29, 29, w^{2} - 7]$ | $\phantom{-}7$ |
29 | $[29, 29, -w^{2} + 2w + 8]$ | $-6$ |
31 | $[31, 31, -2w^{2} + w + 12]$ | $-7$ |
31 | $[31, 31, 2w^{2} - 3w - 11]$ | $\phantom{-}8$ |
41 | $[41, 41, -w]$ | $\phantom{-}1$ |
41 | $[41, 41, -w + 1]$ | $-11$ |
49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $-1$ |
49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $-4$ |
61 | $[61, 61, 2w^{2} - 3w - 14]$ | $-8$ |
61 | $[61, 61, 2w^{2} - w - 15]$ | $\phantom{-}10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, w + 1]$ | $-1$ |