Base field 4.4.13725.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 13 x^2 + x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, w^3 - 4 w^2 - 5 w + 20]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -2 w^3 + 6 w^2 + 13 w - 26]$ | $-5$ |
| 11 | $[11, 11, w^2 - w - 8]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -4 w^3 + 13 w^2 + 23 w - 55]$ | $-3$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 19 | $[19, 19, -w - 1]$ | $-7$ |
| 19 | $[19, 19, -w^3 + 3 w^2 + 7 w - 14]$ | $\phantom{-}5$ |
| 19 | $[19, 19, w^3 - 4 w^2 - 5 w + 20]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -3 w^3 + 10 w^2 + 17 w - 43]$ | $\phantom{-}2$ |
| 25 | $[25, 5, -w^3 + 3 w^2 + 6 w - 10]$ | $\phantom{-}2$ |
| 29 | $[29, 29, 4 w^3 - 13 w^2 - 23 w + 57]$ | $\phantom{-}3$ |
| 29 | $[29, 29, w^2 - w - 6]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -2 w^3 + 7 w^2 + 11 w - 31]$ | $-4$ |
| 31 | $[31, 31, -2 w^3 + 7 w^2 + 11 w - 32]$ | $-4$ |
| 41 | $[41, 41, 3 w^3 - 10 w^2 - 18 w + 43]$ | $\phantom{-}6$ |
| 41 | $[41, 41, 3 w^3 - 9 w^2 - 19 w + 37]$ | $\phantom{-}9$ |
| 41 | $[41, 41, 2 w^3 - 6 w^2 - 11 w + 24]$ | $\phantom{-}0$ |
| 41 | $[41, 41, -2 w^3 + 7 w^2 + 12 w - 33]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 3 w^3 - 10 w^2 - 17 w + 46]$ | $-12$ |
| 59 | $[59, 59, -w^3 + 4 w^2 + 5 w - 17]$ | $-6$ |
| 61 | $[61, 61, 4 w^3 - 12 w^2 - 25 w + 50]$ | $-1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^3 - 4 w^2 - 5 w + 20]$ | $-1$ |