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: | $24$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $151$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{24} - 21x^{23} + 137x^{22} + 117x^{21} - 5345x^{20} + 18149x^{19} + 45150x^{18} - 392175x^{17} + 336664x^{16} + 3063664x^{15} - 7348822x^{14} - 9002368x^{13} + 46187727x^{12} - 6256324x^{11} - 144456207x^{10} + 103883252x^{9} + 249122160x^{8} - 259585548x^{7} - 245763642x^{6} + 286192158x^{5} + 143573041x^{4} - 130950072x^{3} - 47081024x^{2} + 8218496x + 528128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $-1$ |
| 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 |
|---|---|---|
| $7$ | $[7, 7, w - 7]$ | $1$ |
| $7$ | $[7, 7, w + 6]$ | $1$ |