Base field 4.4.14656.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 4 x^2 + 4 x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[15, 15, -w^2 + 2 w + 3]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $-1$ |
| 5 | $[5, 5, -w^2 + w + 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^2 - 3]$ | $-4$ |
| 17 | $[17, 17, -w^2 + w + 3]$ | $-2$ |
| 19 | $[19, 19, -w^3 + 2 w^2 + 3 w - 1]$ | $\phantom{-}0$ |
| 27 | $[27, 3, w^3 - 3 w^2 - w + 5]$ | $\phantom{-}8$ |
| 41 | $[41, 41, -w^3 + 2 w^2 + w - 1]$ | $\phantom{-}2$ |
| 41 | $[41, 41, -w^3 + w^2 + 2 w - 1]$ | $\phantom{-}2$ |
| 43 | $[43, 43, w^3 - w^2 - 5 w + 1]$ | $-4$ |
| 47 | $[47, 47, w^2 - 2 w - 5]$ | $-12$ |
| 47 | $[47, 47, -2 w^3 + 6 w^2 + w - 5]$ | $\phantom{-}0$ |
| 61 | $[61, 61, -2 w^3 + 5 w^2 + 4 w - 7]$ | $-10$ |
| 67 | $[67, 67, -2 w^2 + 2 w + 9]$ | $\phantom{-}4$ |
| 67 | $[67, 67, -w^3 + 2 w^2 + 4 w - 1]$ | $-8$ |
| 71 | $[71, 71, w^3 - w^2 - 6 w + 3]$ | $-4$ |
| 83 | $[83, 83, -w^3 + 2 w^2 + 5 w + 1]$ | $-12$ |
| 89 | $[89, 89, -w - 3]$ | $\phantom{-}6$ |
| 89 | $[89, 89, -w^2 - 2 w + 1]$ | $\phantom{-}6$ |
| 97 | $[97, 97, w^3 - w^2 - 6 w + 1]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $1$ |
| $5$ | $[5, 5, -w^2 + w + 1]$ | $-1$ |