Base field \(\Q(\zeta_{13})^+\)
Generator \(w\), with minimal polynomial \(x^6 - x^5 - 5 x^4 + 4 x^3 + 6 x^2 - 3 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[79,79,w^5 - 3 w^3 - w^2 + 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, w^5 - 5 w^3 + 4 w]$ | $\phantom{-}4$ |
| 25 | $[25, 5, w^5 - 5 w^3 + 6 w - 1]$ | $\phantom{-}6$ |
| 25 | $[25, 5, -w^3 + w^2 + 3 w - 1]$ | $-4$ |
| 25 | $[25, 5, w^5 - 4 w^3 - w^2 + 3 w + 2]$ | $-4$ |
| 27 | $[27, 3, w^4 - w^3 - 4 w^2 + 2 w + 2]$ | $\phantom{-}8$ |
| 27 | $[27, 3, w^4 - w^3 - 4 w^2 + 2 w + 3]$ | $\phantom{-}8$ |
| 53 | $[53, 53, -w^4 + w^3 + 3 w^2 - 2 w + 1]$ | $-6$ |
| 53 | $[53, 53, -w^4 + w^3 + 4 w^2 - 3 w - 4]$ | $-6$ |
| 53 | $[53, 53, -w^5 + w^4 + 4 w^3 - 4 w^2 - 3 w + 1]$ | $\phantom{-}4$ |
| 53 | $[53, 53, w^3 - 2 w - 2]$ | $-6$ |
| 53 | $[53, 53, w^5 - 5 w^3 - w^2 + 5 w]$ | $-6$ |
| 53 | $[53, 53, -w^4 + 4 w^2 + w - 4]$ | $\phantom{-}4$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}5$ |
| 79 | $[79, 79, -2 w^5 + w^4 + 9 w^3 - 3 w^2 - 9 w + 2]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -w^5 - w^4 + 5 w^3 + 4 w^2 - 6 w - 1]$ | $\phantom{-}10$ |
| 79 | $[79, 79, w^3 - w^2 - 4 w + 1]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -2 w^5 + 2 w^4 + 9 w^3 - 7 w^2 - 9 w + 3]$ | $-1$ |
| 79 | $[79, 79, -2 w^4 + w^3 + 7 w^2 - 3 w - 3]$ | $\phantom{-}10$ |
| 79 | $[79, 79, -w^5 + 6 w^3 - w^2 - 8 w + 1]$ | $\phantom{-}0$ |
| 103 | $[103, 103, 2 w^4 - 7 w^2 - w + 3]$ | $-6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $79$ | $[79,79,w^5 - 3 w^3 - w^2 + 2]$ | $1$ |