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: | $[3,3,w - 7]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 34x^{4} + 364x^{2} - 1250\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{27}{5}e^{2} + 33$ |
| 3 | $[3, 3, -w - 7]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{27}{5}e^{2} + 34$ |
| 3 | $[3, 3, w - 7]$ | $-1$ |
| 5 | $[5, 5, -9w + 61]$ | $-\frac{4}{25}e^{5} + \frac{101}{25}e^{3} - \frac{586}{25}e$ |
| 5 | $[5, 5, -9w - 61]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 27]$ | $\phantom{-}\frac{3}{25}e^{5} - \frac{72}{25}e^{3} + \frac{382}{25}e$ |
| 7 | $[7, 7, 4w + 27]$ | $-\frac{4}{25}e^{5} + \frac{96}{25}e^{3} - \frac{501}{25}e$ |
| 23 | $[23, 23, 78w - 529]$ | $-\frac{13}{25}e^{5} + \frac{332}{25}e^{3} - \frac{1887}{25}e$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}\frac{11}{25}e^{5} - \frac{274}{25}e^{3} + \frac{1529}{25}e$ |
| 37 | $[37, 37, w - 3]$ | $-\frac{19}{25}e^{5} + \frac{481}{25}e^{3} - \frac{2761}{25}e$ |
| 41 | $[41, 41, -2w + 15]$ | $\phantom{-}e^{2} - 8$ |
| 41 | $[41, 41, 2w + 15]$ | $-e^{4} + 24e^{2} - 132$ |
| 53 | $[53, 53, -3w - 19]$ | $\phantom{-}\frac{11}{25}e^{5} - \frac{279}{25}e^{3} + \frac{1614}{25}e$ |
| 53 | $[53, 53, 3w - 19]$ | $\phantom{-}\frac{3}{5}e^{5} - \frac{76}{5}e^{3} + 89e$ |
| 59 | $[59, 59, 11w - 75]$ | $-\frac{7}{5}e^{4} + \frac{184}{5}e^{2} - 214$ |
| 59 | $[59, 59, -11w - 75]$ | $-\frac{11}{5}e^{4} + \frac{272}{5}e^{2} - 300$ |
| 61 | $[61, 61, -5w + 33]$ | $-\frac{22}{25}e^{5} + \frac{553}{25}e^{3} - \frac{3118}{25}e$ |
| 61 | $[61, 61, 5w + 33]$ | $-\frac{3}{25}e^{5} + \frac{67}{25}e^{3} - \frac{322}{25}e$ |
| 73 | $[73, 73, -24w - 163]$ | $-\frac{7}{5}e^{4} + \frac{184}{5}e^{2} - 214$ |
| 73 | $[73, 73, -24w + 163]$ | $\phantom{-}\frac{7}{5}e^{4} - \frac{184}{5}e^{2} + 218$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w - 7]$ | $1$ |