Base field 6.6.300125.1
Generator \(w\), with minimal polynomial \(x^6 - x^5 - 7 x^4 + 2 x^3 + 7 x^2 - 2 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $1$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 29 | $[29, 29, -9 w^5 + 3 w^4 + 64 w^3 + 26 w^2 - 40 w - 10]$ | $-7$ |
| 29 | $[29, 29, w^5 - 7 w^3 - 5 w^2 + 2 w + 2]$ | $-7$ |
| 29 | $[29, 29, w^4 - w^3 - 6 w^2 + 2]$ | $-7$ |
| 29 | $[29, 29, 5 w^5 - w^4 - 36 w^3 - 19 w^2 + 21 w + 9]$ | $-7$ |
| 29 | $[29, 29, -w^5 + w^4 + 7 w^3 - 2 w^2 - 6 w + 1]$ | $-7$ |
| 29 | $[29, 29, 2 w^5 - 15 w^3 - 10 w^2 + 11 w + 5]$ | $-7$ |
| 41 | $[41, 41, 5 w^5 - w^4 - 36 w^3 - 18 w^2 + 21 w + 5]$ | $\phantom{-}5$ |
| 41 | $[41, 41, -5 w^5 + 2 w^4 + 36 w^3 + 11 w^2 - 25 w - 2]$ | $\phantom{-}5$ |
| 41 | $[41, 41, 6 w^5 - w^4 - 44 w^3 - 23 w^2 + 30 w + 8]$ | $\phantom{-}5$ |
| 41 | $[41, 41, 13 w^5 - 4 w^4 - 93 w^3 - 39 w^2 + 59 w + 16]$ | $\phantom{-}5$ |
| 41 | $[41, 41, -4 w^5 + 30 w^3 + 19 w^2 - 19 w - 8]$ | $\phantom{-}5$ |
| 41 | $[41, 41, w^5 - 7 w^3 - 6 w^2 + 2 w + 3]$ | $\phantom{-}5$ |
| 49 | $[49, 7, -5 w^5 + w^4 + 36 w^3 + 19 w^2 - 22 w - 6]$ | $\phantom{-}13$ |
| 64 | $[64, 2, -2]$ | $-9$ |
| 71 | $[71, 71, -8 w^5 + w^4 + 58 w^3 + 34 w^2 - 34 w - 16]$ | $-2$ |
| 71 | $[71, 71, -6 w^5 + 2 w^4 + 42 w^3 + 18 w^2 - 23 w - 6]$ | $-2$ |
| 71 | $[71, 71, -8 w^5 + 2 w^4 + 58 w^3 + 27 w^2 - 38 w - 10]$ | $-2$ |
| 71 | $[71, 71, 4 w^5 - 30 w^3 - 19 w^2 + 20 w + 8]$ | $-2$ |
| 71 | $[71, 71, -10 w^5 + 3 w^4 + 72 w^3 + 30 w^2 - 48 w - 10]$ | $-2$ |
| 71 | $[71, 71, -8 w^5 + 2 w^4 + 58 w^3 + 26 w^2 - 37 w - 8]$ | $-2$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).