Base field 4.4.4205.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 5 x^2 - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[49,49,2 w^3 - 3 w^2 - 7 w]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^3 + w^2 + 5 w]$ | $\phantom{-}2$ |
| 7 | $[7, 7, -w^3 + 2 w^2 + 3 w - 3]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^3 - 2 w^2 - 3 w]$ | $-2$ |
| 13 | $[13, 13, -w^2 + w + 3]$ | $-6$ |
| 13 | $[13, 13, -w^2 + w + 2]$ | $-4$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}3$ |
| 23 | $[23, 23, -w^2 + 3 w + 1]$ | $-4$ |
| 23 | $[23, 23, -2 w^3 + 3 w^2 + 9 w - 2]$ | $-6$ |
| 25 | $[25, 5, w^3 - 2 w^2 - 2 w + 2]$ | $\phantom{-}6$ |
| 49 | $[49, 7, w^3 - w^2 - 6 w - 1]$ | $-10$ |
| 53 | $[53, 53, 2 w^3 - 2 w^2 - 8 w - 3]$ | $-6$ |
| 53 | $[53, 53, 2 w^3 - 2 w^2 - 8 w - 1]$ | $\phantom{-}4$ |
| 67 | $[67, 67, 2 w^3 - 4 w^2 - 7 w + 2]$ | $-12$ |
| 67 | $[67, 67, -2 w^3 + 4 w^2 + 6 w - 1]$ | $\phantom{-}12$ |
| 81 | $[81, 3, -3]$ | $-8$ |
| 83 | $[83, 83, 2 w^3 - 3 w^2 - 6 w - 1]$ | $\phantom{-}4$ |
| 83 | $[83, 83, 3 w^3 - 4 w^2 - 12 w + 1]$ | $\phantom{-}6$ |
| 103 | $[103, 103, 3 w^3 - 4 w^2 - 12 w - 1]$ | $\phantom{-}16$ |
| 103 | $[103, 103, 2 w^3 - 3 w^2 - 6 w + 1]$ | $\phantom{-}4$ |
| 107 | $[107, 107, w^3 - w^2 - 3 w - 3]$ | $-18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-w^3 + 2 w^2 + 3 w - 3]$ | $-1$ |