Base field \(\Q(\sqrt{101}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[25, 5, 5]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 2x^{6} - 13x^{5} - 15x^{4} + 60x^{3} + 14x^{2} - 98x + 47\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w - 4]$ | $-1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{6} + 3e^{5} - 9e^{4} - 23e^{3} + 26e^{2} + 38e - 32$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}18e^{6} + 60e^{5} - 153e^{4} - 473e^{3} + 439e^{2} + 835e - 628$ |
| 13 | $[13, 13, w - 4]$ | $-6e^{6} - 20e^{5} + 51e^{4} + 157e^{3} - 147e^{2} - 275e + 210$ |
| 17 | $[17, 17, w + 6]$ | $-8e^{6} - 27e^{5} + 67e^{4} + 213e^{3} - 188e^{2} - 378e + 271$ |
| 17 | $[17, 17, -w + 7]$ | $-4e^{6} - 13e^{5} + 35e^{4} + 103e^{3} - 104e^{2} - 184e + 145$ |
| 19 | $[19, 19, w + 2]$ | $-14e^{6} - 47e^{5} + 118e^{4} + 370e^{3} - 333e^{2} - 649e + 471$ |
| 19 | $[19, 19, w - 3]$ | $-14e^{6} - 47e^{5} + 118e^{4} + 370e^{3} - 337e^{2} - 653e + 487$ |
| 23 | $[23, 23, w + 1]$ | $\phantom{-}20e^{6} + 67e^{5} - 169e^{4} - 527e^{3} + 482e^{2} + 926e - 687$ |
| 23 | $[23, 23, -w + 2]$ | $-4e^{6} - 13e^{5} + 35e^{4} + 103e^{3} - 104e^{2} - 184e + 145$ |
| 31 | $[31, 31, -w - 7]$ | $\phantom{-}8e^{6} + 27e^{5} - 66e^{4} - 211e^{3} + 180e^{2} + 368e - 258$ |
| 31 | $[31, 31, w - 8]$ | $-4e^{6} - 13e^{5} + 34e^{4} + 101e^{3} - 96e^{2} - 176e + 130$ |
| 37 | $[37, 37, 2w - 9]$ | $\phantom{-}15e^{6} + 51e^{5} - 125e^{4} - 401e^{3} + 353e^{2} + 706e - 513$ |
| 37 | $[37, 37, 2w + 7]$ | $-5e^{6} - 17e^{5} + 43e^{4} + 137e^{3} - 127e^{2} - 250e + 185$ |
| 43 | $[43, 43, 4w + 17]$ | $-19e^{6} - 64e^{5} + 159e^{4} + 502e^{3} - 449e^{2} - 878e + 643$ |
| 43 | $[43, 43, 4w - 21]$ | $\phantom{-}31e^{6} + 104e^{5} - 263e^{4} - 822e^{3} + 757e^{2} + 1456e - 1095$ |
| 47 | $[47, 47, -w - 8]$ | $-4e^{6} - 13e^{5} + 33e^{4} + 98e^{3} - 88e^{2} - 161e + 113$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}18e^{6} + 61e^{5} - 151e^{4} - 482e^{3} + 430e^{2} + 855e - 631$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w + 5]$ | $-1$ |
| $5$ | $[5, 5, -w - 4]$ | $1$ |