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: | $[4,4,w - 10]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} + 18x^{12} + 120x^{10} + 372x^{8} + 555x^{6} + 393x^{4} + 121x^{2} + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{2}{3}e^{12} - \frac{34}{3}e^{10} - \frac{208}{3}e^{8} - \frac{563}{3}e^{6} - \frac{662}{3}e^{4} - \frac{301}{3}e^{2} - 12$ |
| 11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{1}{6}e^{13} + 3e^{11} + \frac{61}{3}e^{9} + 66e^{7} + \frac{631}{6}e^{5} + \frac{141}{2}e^{3} + \frac{19}{2}e$ |
| 11 | $[11, 11, w + 8]$ | $\phantom{-}e^{13} + \frac{53}{3}e^{11} + 114e^{9} + \frac{997}{3}e^{7} + 436e^{5} + \frac{698}{3}e^{3} + 36e$ |
| 13 | $[13, 13, 4w - 41]$ | $\phantom{-}\frac{1}{3}e^{10} + 5e^{8} + \frac{77}{3}e^{6} + 55e^{4} + \frac{142}{3}e^{2} + 11$ |
| 19 | $[19, 19, w + 7]$ | $-\frac{5}{6}e^{13} - 15e^{11} - \frac{299}{3}e^{9} - 305e^{7} - \frac{2621}{6}e^{5} - \frac{545}{2}e^{3} - \frac{107}{2}e$ |
| 19 | $[19, 19, w + 11]$ | $\phantom{-}\frac{4}{3}e^{13} + 23e^{11} + \frac{428}{3}e^{9} + 388e^{7} + \frac{1336}{3}e^{5} + 183e^{3} + 11e$ |
| 23 | $[23, 23, -2w + 21]$ | $\phantom{-}\frac{1}{3}e^{12} + \frac{17}{3}e^{10} + \frac{104}{3}e^{8} + \frac{280}{3}e^{6} + \frac{313}{3}e^{4} + \frac{95}{3}e^{2} - 4$ |
| 23 | $[23, 23, -2w - 19]$ | $-\frac{1}{3}e^{12} - \frac{19}{3}e^{10} - \frac{134}{3}e^{8} - \frac{434}{3}e^{6} - \frac{643}{3}e^{4} - \frac{373}{3}e^{2} - 16$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{3}e^{12} + \frac{17}{3}e^{10} + \frac{101}{3}e^{8} + \frac{244}{3}e^{6} + \frac{196}{3}e^{4} + \frac{17}{3}e^{2} - 3$ |
| 29 | $[29, 29, 6w - 61]$ | $-\frac{4}{3}e^{12} - 23e^{10} - \frac{431}{3}e^{8} - 401e^{6} - \frac{1489}{3}e^{4} - 248e^{2} - 33$ |
| 31 | $[31, 31, w + 12]$ | $\phantom{-}\frac{2}{3}e^{13} + \frac{34}{3}e^{11} + \frac{208}{3}e^{9} + \frac{563}{3}e^{7} + \frac{662}{3}e^{5} + \frac{301}{3}e^{3} + 9e$ |
| 31 | $[31, 31, w + 18]$ | $-\frac{11}{6}e^{13} - 32e^{11} - \frac{605}{3}e^{9} - 560e^{7} - \frac{3959}{6}e^{5} - \frac{551}{2}e^{3} - \frac{37}{2}e$ |
| 37 | $[37, 37, w + 4]$ | $-2e^{13} - \frac{106}{3}e^{11} - 228e^{9} - \frac{1994}{3}e^{7} - 872e^{5} - \frac{1399}{3}e^{3} - 76e$ |
| 37 | $[37, 37, w + 32]$ | $\phantom{-}\frac{1}{2}e^{13} + \frac{28}{3}e^{11} + 65e^{9} + \frac{635}{3}e^{7} + \frac{665}{2}e^{5} + \frac{1445}{6}e^{3} + \frac{115}{2}e$ |
| 41 | $[41, 41, w + 3]$ | $\phantom{-}\frac{7}{6}e^{13} + \frac{59}{3}e^{11} + \frac{352}{3}e^{9} + \frac{889}{3}e^{7} + \frac{1711}{6}e^{5} + \frac{397}{6}e^{3} - \frac{17}{2}e$ |
| 41 | $[41, 41, w + 37]$ | $-2e^{13} - 35e^{11} - 223e^{9} - 640e^{7} - 828e^{5} - 451e^{3} - 84e$ |
| 47 | $[47, 47, w]$ | $-\frac{7}{3}e^{13} - 41e^{11} - \frac{785}{3}e^{9} - 745e^{7} - \frac{2776}{3}e^{5} - 433e^{3} - 47e$ |
| 47 | $[47, 47, w + 46]$ | $-3e^{13} - \frac{157}{3}e^{11} - 331e^{9} - \frac{2801}{3}e^{7} - 1158e^{5} - \frac{1717}{3}e^{3} - 85e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 2]$ | $1$ |