Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[13, 13, -2w + 11]$ |
| Dimension: | $13$ |
| 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:
| \(x^{13} + x^{12} - 19x^{11} - 15x^{10} + 134x^{9} + 73x^{8} - 433x^{7} - 125x^{6} + 631x^{5} + 54x^{4} - 337x^{3} - 35x^{2} + 58x + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $...$ |
| 2 | $[2, 2, w + 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 6w - 35]$ | $-\frac{424}{47}e^{12} - \frac{900}{47}e^{11} + \frac{7074}{47}e^{10} + \frac{14353}{47}e^{9} - \frac{41198}{47}e^{8} - \frac{78014}{47}e^{7} + \frac{99122}{47}e^{6} + \frac{168567}{47}e^{5} - \frac{86867}{47}e^{4} - \frac{128994}{47}e^{3} + \frac{7795}{47}e^{2} + \frac{28757}{47}e + \frac{4976}{47}$ |
| 7 | $[7, 7, -6w - 29]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, 4w + 19]$ | $...$ |
| 11 | $[11, 11, 4w - 23]$ | $...$ |
| 13 | $[13, 13, -2w + 11]$ | $\phantom{-}1$ |
| 13 | $[13, 13, 2w + 9]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 31 | $[31, 31, 2w - 13]$ | $...$ |
| 31 | $[31, 31, -2w - 11]$ | $...$ |
| 41 | $[41, 41, -8w - 39]$ | $...$ |
| 41 | $[41, 41, 8w - 47]$ | $...$ |
| 53 | $[53, 53, -26w - 125]$ | $...$ |
| 53 | $[53, 53, 26w - 151]$ | $...$ |
| 61 | $[61, 61, -14w + 81]$ | $...$ |
| 61 | $[61, 61, -14w - 67]$ | $...$ |
| 83 | $[83, 83, 2w - 15]$ | $...$ |
| 83 | $[83, 83, -2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -2w + 11]$ | $-1$ |