Base field \(\Q(\sqrt{15}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7,7,-w + 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 36x^{6} + 330x^{4} + 684x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{3}{104}e^{7} + \frac{25}{24}e^{5} + \frac{1003}{104}e^{3} + \frac{2123}{104}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{3}{104}e^{7} + \frac{25}{24}e^{5} + \frac{1003}{104}e^{3} + \frac{2227}{104}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{52}e^{7} + \frac{2}{3}e^{5} + \frac{291}{52}e^{3} + \frac{239}{26}e$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{1}{36}e^{7} - e^{5} - \frac{109}{12}e^{3} - \frac{35}{2}e$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}\frac{1}{72}e^{7} + \frac{1}{2}e^{5} + \frac{109}{24}e^{3} + \frac{35}{4}e$ |
| 11 | $[11, 11, -w - 2]$ | $-\frac{1}{312}e^{6} - \frac{1}{8}e^{4} - \frac{175}{104}e^{2} - \frac{597}{104}$ |
| 11 | $[11, 11, w - 2]$ | $-\frac{1}{104}e^{6} - \frac{7}{24}e^{4} - \frac{161}{104}e^{2} + \frac{107}{104}$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}\frac{1}{13}e^{7} + \frac{11}{4}e^{5} + \frac{647}{26}e^{3} + \frac{2601}{52}e$ |
| 17 | $[17, 17, w + 10]$ | $-\frac{1}{52}e^{7} - \frac{2}{3}e^{5} - \frac{291}{52}e^{3} - \frac{239}{26}e$ |
| 43 | $[43, 43, w + 12]$ | $-\frac{1}{936}e^{7} - \frac{1}{24}e^{5} - \frac{175}{312}e^{3} - \frac{407}{104}e$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{29}{936}e^{7} - \frac{9}{8}e^{5} - \frac{3359}{312}e^{3} - \frac{3041}{104}e$ |
| 53 | $[53, 53, w + 11]$ | $\phantom{-}\frac{3}{52}e^{7} + 2e^{5} + \frac{873}{52}e^{3} + \frac{717}{26}e$ |
| 53 | $[53, 53, w + 42]$ | $\phantom{-}\frac{3}{52}e^{7} + \frac{13}{6}e^{5} + \frac{1133}{52}e^{3} + \frac{703}{13}e$ |
| 59 | $[59, 59, 2w - 1]$ | $\phantom{-}\frac{1}{24}e^{6} + \frac{31}{24}e^{4} + \frac{63}{8}e^{2} + \frac{13}{8}$ |
| 59 | $[59, 59, -2w - 1]$ | $-\frac{11}{312}e^{6} - \frac{9}{8}e^{4} - \frac{833}{104}e^{2} - \frac{873}{104}$ |
| 61 | $[61, 61, 2w - 11]$ | $-8$ |
| 61 | $[61, 61, -2w - 11]$ | $\phantom{-}\frac{1}{78}e^{6} + \frac{1}{2}e^{4} + \frac{123}{26}e^{2} + \frac{389}{26}$ |
| 67 | $[67, 67, w + 22]$ | $\phantom{-}\frac{53}{936}e^{7} + \frac{49}{24}e^{5} + \frac{5843}{312}e^{3} + \frac{4047}{104}e$ |
| 67 | $[67, 67, w + 45]$ | $-\frac{77}{936}e^{7} - \frac{71}{24}e^{5} - \frac{8327}{312}e^{3} - \frac{5053}{104}e$ |
| 71 | $[71, 71, 3w - 8]$ | $\phantom{-}\frac{1}{26}e^{6} + \frac{7}{6}e^{4} + \frac{161}{26}e^{2} - \frac{107}{26}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-w + 1]$ | $-\frac{1}{72}e^{7} - \frac{1}{2}e^{5} - \frac{109}{24}e^{3} - \frac{35}{4}e$ |