Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[25, 5, 5]$ |
| Dimension: | $33$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $99$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{33} - 33x^{32} + 425x^{31} - 2193x^{30} - 4367x^{29} + 113495x^{28} - 460321x^{27} - 766115x^{26} + 12259355x^{25} - 28137249x^{24} - 89459227x^{23} + 571061493x^{22} - 459952616x^{21} - 3872899170x^{20} + 10871922192x^{19} + 4343552800x^{18} - 62878423234x^{17} + 73530190820x^{16} + 127314247505x^{15} - 369377155851x^{14} + 91614575115x^{13} + 618813978923x^{12} - 640805692978x^{11} - 269291975916x^{10} + 676319373972x^{9} - 65021472964x^{8} - 322285989173x^{7} + 68881727837x^{6} + 87805765986x^{5} - 12789145774x^{4} - 13755210999x^{3} - 268653335x^{2} + 742367532x + 89467264\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $...$ |
| 7 | $[7, 7, w + 6]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 19 | $[19, 19, w + 5]$ | $...$ |
| 19 | $[19, 19, w - 6]$ | $...$ |
| 23 | $[23, 23, w + 8]$ | $...$ |
| 23 | $[23, 23, -w + 9]$ | $...$ |
| 25 | $[25, 5, 5]$ | $-1$ |
| 29 | $[29, 29, -w - 4]$ | $...$ |
| 29 | $[29, 29, w - 5]$ | $...$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w - 4]$ | $...$ |
| 41 | $[41, 41, -w - 9]$ | $...$ |
| 41 | $[41, 41, w - 10]$ | $...$ |
| 43 | $[43, 43, -w - 2]$ | $...$ |
| 43 | $[43, 43, w - 3]$ | $...$ |
| 47 | $[47, 47, -w - 1]$ | $...$ |
| 47 | $[47, 47, w - 2]$ | $...$ |
| 53 | $[53, 53, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, 5]$ | $1$ |