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: | $[49, 7, 7]$ |
| Dimension: | $34$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $151$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{34} + x^{33} - 79x^{32} - 65x^{31} + 2807x^{30} + 1857x^{29} - 59290x^{28} - 30729x^{27} + 829156x^{26} + 327076x^{25} - 8094177x^{24} - 2357767x^{23} + 56669087x^{22} + 11884380x^{21} - 287877466x^{20} - 43360641x^{19} + 1061405138x^{18} + 121955919x^{17} - 2812379435x^{16} - 290869096x^{15} + 5244750771x^{14} + 612633895x^{13} - 6648604541x^{12} - 1029005994x^{11} + 5422877464x^{10} + 1165061358x^{9} - 2606715364x^{8} - 756164192x^{7} + 636815427x^{6} + 232770800x^{5} - 59420559x^{4} - 26680508x^{3} + 1177893x^{2} + 933994x + 34751\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 6]$ | $-1$ |
| 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 | $[25, 5, 5]$ | $...$ |
| 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 |
|---|---|---|
| $7$ | $[7, 7, w - 7]$ | $-1$ |
| $7$ | $[7, 7, w + 6]$ | $1$ |