Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,-5w + 34]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 41x^{6} + 552x^{4} - 2774x^{2} + 4624\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w - 7]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w - 7]$ | $-\frac{1}{27}e^{6} + \frac{13}{9}e^{4} - \frac{149}{9}e^{2} + \frac{1286}{27}$ |
| 5 | $[5, 5, -9w + 61]$ | $-\frac{23}{1836}e^{7} + \frac{269}{612}e^{5} - \frac{667}{153}e^{3} + \frac{9155}{918}e$ |
| 5 | $[5, 5, -9w - 61]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 27]$ | $\phantom{-}\frac{25}{1836}e^{7} - \frac{319}{612}e^{5} + \frac{878}{153}e^{3} - \frac{13663}{918}e$ |
| 7 | $[7, 7, 4w + 27]$ | $\phantom{-}\frac{31}{918}e^{7} - \frac{367}{306}e^{5} + \frac{1900}{153}e^{3} - \frac{15100}{459}e$ |
| 23 | $[23, 23, 78w - 529]$ | $-\frac{35}{612}e^{7} + \frac{433}{204}e^{5} - \frac{395}{17}e^{3} + \frac{20087}{306}e$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}\frac{35}{612}e^{7} - \frac{433}{204}e^{5} + \frac{395}{17}e^{3} - \frac{20699}{306}e$ |
| 37 | $[37, 37, w - 3]$ | $\phantom{-}\frac{91}{1836}e^{7} - \frac{1153}{612}e^{5} + \frac{3200}{153}e^{3} - \frac{53797}{918}e$ |
| 41 | $[41, 41, -2w + 15]$ | $\phantom{-}\frac{1}{27}e^{6} - \frac{10}{9}e^{4} + \frac{74}{9}e^{2} - \frac{278}{27}$ |
| 41 | $[41, 41, 2w + 15]$ | $-\frac{1}{9}e^{6} + 4e^{4} - \frac{124}{3}e^{2} + \frac{968}{9}$ |
| 53 | $[53, 53, -3w - 19]$ | $-\frac{53}{1836}e^{7} + \frac{611}{612}e^{5} - \frac{1588}{153}e^{3} + \frac{28427}{918}e$ |
| 53 | $[53, 53, 3w - 19]$ | $-\frac{29}{306}e^{7} + \frac{117}{34}e^{5} - \frac{1852}{51}e^{3} + \frac{14927}{153}e$ |
| 59 | $[59, 59, 11w - 75]$ | $-\frac{1}{27}e^{6} + \frac{10}{9}e^{4} - \frac{92}{9}e^{2} + \frac{980}{27}$ |
| 59 | $[59, 59, -11w - 75]$ | $\phantom{-}\frac{1}{9}e^{6} - 4e^{4} + \frac{127}{3}e^{2} - \frac{1040}{9}$ |
| 61 | $[61, 61, -5w + 33]$ | $-\frac{52}{459}e^{7} + \frac{637}{153}e^{5} - \frac{6899}{153}e^{3} + \frac{58007}{459}e$ |
| 61 | $[61, 61, 5w + 33]$ | $-2e$ |
| 73 | $[73, 73, -24w - 163]$ | $\phantom{-}\frac{5}{27}e^{6} - \frac{59}{9}e^{4} + \frac{622}{9}e^{2} - \frac{5278}{27}$ |
| 73 | $[73, 73, -24w + 163]$ | $\phantom{-}\frac{1}{27}e^{6} - \frac{10}{9}e^{4} + \frac{83}{9}e^{2} - \frac{386}{27}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-23w - 156]$ | $-1$ |
| $3$ | $[3,3,-w - 7]$ | $-1$ |