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: | $[7,7,-6w - 29]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 3x^{9} - 12x^{8} + 40x^{7} + 37x^{6} - 162x^{5} - 7x^{4} + 199x^{3} - 5x^{2} - 80x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $-\frac{1}{2}e^{8} + 6e^{6} - e^{5} - \frac{41}{2}e^{4} + \frac{15}{2}e^{3} + 18e^{2} - \frac{13}{2}e - 4$ |
| 2 | $[2, 2, w + 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 6w - 35]$ | $-\frac{1}{2}e^{9} + e^{8} + 7e^{7} - 12e^{6} - \frac{61}{2}e^{5} + \frac{79}{2}e^{4} + 44e^{3} - \frac{47}{2}e^{2} - 27e - 4$ |
| 7 | $[7, 7, -6w - 29]$ | $-1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{3}{2}e^{9} - \frac{1}{2}e^{8} - 19e^{7} + 8e^{6} + \frac{145}{2}e^{5} - 34e^{4} - \frac{173}{2}e^{3} + \frac{39}{2}e^{2} + \frac{77}{2}e + 4$ |
| 11 | $[11, 11, 4w + 19]$ | $\phantom{-}\frac{3}{2}e^{9} - e^{8} - 19e^{7} + 14e^{6} + \frac{143}{2}e^{5} - \frac{109}{2}e^{4} - 79e^{3} + \frac{75}{2}e^{2} + 32e - 1$ |
| 11 | $[11, 11, 4w - 23]$ | $-\frac{5}{2}e^{9} + e^{8} + 33e^{7} - 15e^{6} - \frac{271}{2}e^{5} + \frac{123}{2}e^{4} + 187e^{3} - \frac{77}{2}e^{2} - 89e - 12$ |
| 13 | $[13, 13, -2w + 11]$ | $-2e^{9} + 2e^{8} + 27e^{7} - 25e^{6} - 113e^{5} + 85e^{4} + 155e^{3} - 42e^{2} - 79e - 18$ |
| 13 | $[13, 13, 2w + 9]$ | $\phantom{-}\frac{5}{2}e^{9} - 2e^{8} - 34e^{7} + 26e^{6} + \frac{289}{2}e^{5} - \frac{189}{2}e^{4} - 204e^{3} + \frac{127}{2}e^{2} + 94e + 8$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}e^{7} - 12e^{5} + e^{4} + 40e^{3} - 7e^{2} - 29e$ |
| 31 | $[31, 31, 2w - 13]$ | $-\frac{5}{2}e^{9} - e^{8} + 33e^{7} + 9e^{6} - \frac{279}{2}e^{5} - \frac{41}{2}e^{4} + 215e^{3} + \frac{65}{2}e^{2} - 103e - 25$ |
| 31 | $[31, 31, -2w - 11]$ | $-\frac{5}{2}e^{9} + \frac{3}{2}e^{8} + 32e^{7} - 21e^{6} - \frac{247}{2}e^{5} + 82e^{4} + \frac{293}{2}e^{3} - \frac{111}{2}e^{2} - \frac{119}{2}e - 2$ |
| 41 | $[41, 41, -8w - 39]$ | $\phantom{-}\frac{9}{2}e^{9} - \frac{5}{2}e^{8} - 61e^{7} + 33e^{6} + \frac{521}{2}e^{5} - 119e^{4} - \frac{759}{2}e^{3} + \frac{119}{2}e^{2} + \frac{361}{2}e + 32$ |
| 41 | $[41, 41, 8w - 47]$ | $\phantom{-}\frac{1}{2}e^{9} - 2e^{8} - 6e^{7} + 25e^{6} + \frac{35}{2}e^{5} - \frac{179}{2}e^{4} + 3e^{3} + \frac{151}{2}e^{2} - 2e - 10$ |
| 53 | $[53, 53, -26w - 125]$ | $\phantom{-}e^{9} - e^{8} - 13e^{7} + 14e^{6} + 52e^{5} - 57e^{4} - 69e^{3} + 54e^{2} + 37e - 4$ |
| 53 | $[53, 53, 26w - 151]$ | $\phantom{-}\frac{11}{2}e^{9} - 4e^{8} - 74e^{7} + 53e^{6} + \frac{623}{2}e^{5} - \frac{391}{2}e^{4} - 443e^{3} + \frac{247}{2}e^{2} + 225e + 30$ |
| 61 | $[61, 61, -14w + 81]$ | $-e^{9} + 14e^{7} - 65e^{5} - 4e^{4} + 116e^{3} + 30e^{2} - 70e - 26$ |
| 61 | $[61, 61, -14w - 67]$ | $-\frac{11}{2}e^{9} + 3e^{8} + 69e^{7} - 44e^{6} - \frac{513}{2}e^{5} + \frac{355}{2}e^{4} + 280e^{3} - \frac{229}{2}e^{2} - 112e - 17$ |
| 83 | $[83, 83, 2w - 15]$ | $-\frac{3}{2}e^{9} + \frac{1}{2}e^{8} + 23e^{7} - 5e^{6} - \frac{235}{2}e^{5} + 8e^{4} + \frac{447}{2}e^{3} + \frac{55}{2}e^{2} - \frac{257}{2}e - 32$ |
| 83 | $[83, 83, -2w - 13]$ | $\phantom{-}\frac{11}{2}e^{9} - 4e^{8} - 76e^{7} + 51e^{6} + \frac{667}{2}e^{5} - \frac{357}{2}e^{4} - 507e^{3} + \frac{191}{2}e^{2} + 261e + 41$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-6w - 29]$ | $1$ |