Base field 5.5.179024.1
Generator \(w\), with minimal polynomial \(x^{5} - 8x^{3} + 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[18, 18, 3w^{4} + 2w^{3} - 23w^{2} - 15w + 12]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
3 | $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$ | $\phantom{-}0$ |
11 | $[11, 11, 2w^{4} + w^{3} - 16w^{2} - 9w + 9]$ | $\phantom{-}6$ |
17 | $[17, 17, w^{4} + w^{3} - 8w^{2} - 6w + 5]$ | $\phantom{-}3$ |
29 | $[29, 29, w^{4} - 8w^{2} + 3]$ | $\phantom{-}6$ |
43 | $[43, 43, 6w^{4} + 3w^{3} - 46w^{2} - 24w + 21]$ | $-7$ |
43 | $[43, 43, 2w^{4} + w^{3} - 15w^{2} - 6w + 7]$ | $\phantom{-}8$ |
47 | $[47, 47, 3w^{4} + w^{3} - 23w^{2} - 9w + 11]$ | $-3$ |
47 | $[47, 47, w^{4} + w^{3} - 8w^{2} - 7w + 3]$ | $-6$ |
49 | $[49, 7, -w^{4} + 8w^{2} + 2w - 5]$ | $-10$ |
53 | $[53, 53, -6w^{4} - 3w^{3} + 46w^{2} + 23w - 23]$ | $\phantom{-}6$ |
53 | $[53, 53, 2w^{4} + w^{3} - 15w^{2} - 7w + 5]$ | $\phantom{-}9$ |
59 | $[59, 59, 13w^{4} + 7w^{3} - 101w^{2} - 54w + 55]$ | $\phantom{-}3$ |
67 | $[67, 67, 5w^{4} + 3w^{3} - 39w^{2} - 23w + 19]$ | $\phantom{-}8$ |
67 | $[67, 67, 4w^{4} + 2w^{3} - 32w^{2} - 16w + 19]$ | $\phantom{-}14$ |
71 | $[71, 71, 4w^{4} + 3w^{3} - 31w^{2} - 22w + 15]$ | $-9$ |
71 | $[71, 71, 9w^{4} + 5w^{3} - 70w^{2} - 38w + 39]$ | $\phantom{-}3$ |
71 | $[71, 71, 4w^{4} + w^{3} - 31w^{2} - 8w + 17]$ | $\phantom{-}15$ |
81 | $[81, 3, -5w^{4} - 2w^{3} + 38w^{2} + 17w - 19]$ | $\phantom{-}10$ |
83 | $[83, 83, -3w^{4} - w^{3} + 24w^{2} + 9w - 13]$ | $-15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $1$ |
$3$ | $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$ | $-1$ |