Base field \(\Q(\sqrt{377}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 9x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{1}{4}e^{3} - \frac{5}{4}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $-e^{2} - 6$ |
| 11 | $[11, 11, w + 2]$ | $-\frac{3}{4}e^{3} - \frac{15}{4}e$ |
| 11 | $[11, 11, w + 8]$ | $\phantom{-}e$ |
| 13 | $[13, 13, 4w - 41]$ | $\phantom{-}3$ |
| 19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{9}{4}e$ |
| 19 | $[19, 19, w + 11]$ | $\phantom{-}e^{3} + 5e$ |
| 23 | $[23, 23, -2w + 21]$ | $\phantom{-}2e^{2} + 8$ |
| 23 | $[23, 23, -2w - 19]$ | $\phantom{-}6$ |
| 25 | $[25, 5, -5]$ | $-1$ |
| 29 | $[29, 29, 6w - 61]$ | $\phantom{-}e^{2} + 11$ |
| 31 | $[31, 31, w + 12]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e$ |
| 31 | $[31, 31, w + 18]$ | $-\frac{1}{4}e^{3} - \frac{5}{4}e$ |
| 37 | $[37, 37, w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{9}{2}e$ |
| 37 | $[37, 37, w + 32]$ | $-\frac{3}{4}e^{3} - \frac{11}{4}e$ |
| 41 | $[41, 41, w + 3]$ | $-\frac{7}{4}e^{3} - \frac{39}{4}e$ |
| 41 | $[41, 41, w + 37]$ | $-\frac{1}{2}e^{3} - \frac{13}{2}e$ |
| 47 | $[47, 47, w]$ | $\phantom{-}e^{3} + 6e$ |
| 47 | $[47, 47, w + 46]$ | $\phantom{-}e^{3} + 4e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{1}{4}e^{3} + \frac{5}{4}e$ |