Base field 6.6.703493.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
13 | $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ | $-3$ |
13 | $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ | $\phantom{-}2$ |
13 | $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ | $-6$ |
13 | $[13, 13, -w^{2} + 3]$ | $-1$ |
41 | $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ | $-10$ |
41 | $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ | $-5$ |
41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $\phantom{-}3$ |
41 | $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ | $\phantom{-}3$ |
43 | $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ | $\phantom{-}5$ |
43 | $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ | $\phantom{-}5$ |
49 | $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ | $\phantom{-}11$ |
64 | $[64, 2, -2]$ | $-9$ |
71 | $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ | $-1$ |
71 | $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ | $-7$ |
83 | $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ | $-14$ |
83 | $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ | $\phantom{-}16$ |
97 | $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ | $-5$ |
97 | $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ | $\phantom{-}5$ |
113 | $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ | $-6$ |
113 | $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ | $\phantom{-}3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$71$ | $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ | $1$ |