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: | $[23,23,-w + 9]$ |
| Dimension: | $34$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $81$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{34} + 6x^{33} - 64x^{32} - 424x^{31} + 1770x^{30} + 13292x^{29} - 27918x^{28} - 245359x^{27} + 279741x^{26} + 2984856x^{25} - 1887901x^{24} - 25363915x^{23} + 9020266x^{22} + 155522086x^{21} - 33007342x^{20} - 699955090x^{19} + 105465900x^{18} + 2325984857x^{17} - 323151722x^{16} - 5685880095x^{15} + 878189527x^{14} + 10090669043x^{13} - 1813609905x^{12} - 12693014291x^{11} + 2537362006x^{10} + 10894619315x^{9} - 2185785281x^{8} - 6016229092x^{7} + 998123180x^{6} + 1946184690x^{5} - 153475734x^{4} - 310007709x^{3} - 16784172x^{2} + 12803090x + 1214263\) |
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 | $[23, 23, -w + 9]$ | $\phantom{-}1$ |
| 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 |
|---|---|---|
| $23$ | $[23,23,-w + 9]$ | $-1$ |