Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w + 3]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} + 3x^{14} - 14x^{13} - 48x^{12} + 61x^{11} + 278x^{10} - 62x^{9} - 734x^{8} - 182x^{7} + 903x^{6} + 445x^{5} - 470x^{4} - 311x^{3} + 64x^{2} + 70x + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $...$ |
| 5 | $[5, 5, w - 1]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $-1$ |
| 13 | $[13, 13, -2w + 1]$ | $...$ |
| 19 | $[19, 19, 2w^{2} - w - 15]$ | $...$ |
| 25 | $[25, 5, w^{2} - 7]$ | $...$ |
| 27 | $[27, 3, 3]$ | $-27e^{14} - 49e^{13} + 435e^{12} + 777e^{11} - 2554e^{10} - 4426e^{9} + 6871e^{8} + 11388e^{7} - 8599e^{6} - 13528e^{5} + 4359e^{4} + 6919e^{3} - 291e^{2} - 1255e - 225$ |
| 31 | $[31, 31, w^{2} - 2w - 1]$ | $...$ |
| 37 | $[37, 37, -3w^{2} + 2w + 23]$ | $...$ |
| 41 | $[41, 41, -2w - 1]$ | $...$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-14e^{14} - 29e^{13} + 219e^{12} + 459e^{11} - 1223e^{10} - 2608e^{9} + 3011e^{8} + 6677e^{7} - 3150e^{6} - 7839e^{5} + 945e^{4} + 3894e^{3} + 297e^{2} - 662e - 140$ |
| 49 | $[49, 7, w^{2} - 2w - 5]$ | $...$ |
| 59 | $[59, 59, 2w - 3]$ | $...$ |
| 67 | $[67, 67, w - 5]$ | $...$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $...$ |
| 73 | $[73, 73, w^{2} + 1]$ | $...$ |
| 83 | $[83, 83, -4w^{2} + 3w + 27]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w + 3]$ | $1$ |