Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $132$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 24x^{10} + 206x^{8} - 796x^{6} + 1433x^{4} - 1092x^{2} + 224\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{32}e^{10} - \frac{21}{32}e^{8} + \frac{143}{32}e^{6} - \frac{359}{32}e^{4} + \frac{61}{8}e^{2} + 1$ |
| 3 | $[3, 3, w + 1]$ | $-e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -3w + 25]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w - 9]$ | $-\frac{5}{16}e^{10} + \frac{111}{16}e^{8} - \frac{831}{16}e^{6} + \frac{2497}{16}e^{4} - \frac{683}{4}e^{2} + 40$ |
| 11 | $[11, 11, -w - 9]$ | $-\frac{5}{16}e^{10} + \frac{111}{16}e^{8} - \frac{831}{16}e^{6} + \frac{2497}{16}e^{4} - \frac{683}{4}e^{2} + 40$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{1}{16}e^{11} - \frac{23}{16}e^{9} + \frac{183}{16}e^{7} - \frac{617}{16}e^{5} + \frac{109}{2}e^{3} - 26e$ |
| 17 | $[17, 17, w + 11]$ | $-\frac{1}{16}e^{11} + \frac{23}{16}e^{9} - \frac{183}{16}e^{7} + \frac{617}{16}e^{5} - \frac{109}{2}e^{3} + 26e$ |
| 23 | $[23, 23, w + 1]$ | $\phantom{-}\frac{5}{16}e^{10} - \frac{111}{16}e^{8} + \frac{831}{16}e^{6} - \frac{2505}{16}e^{4} + \frac{701}{4}e^{2} - 46$ |
| 23 | $[23, 23, w + 22]$ | $\phantom{-}\frac{5}{16}e^{10} - \frac{111}{16}e^{8} + \frac{831}{16}e^{6} - \frac{2505}{16}e^{4} + \frac{701}{4}e^{2} - 46$ |
| 31 | $[31, 31, 4w - 33]$ | $-\frac{1}{8}e^{11} + \frac{11}{4}e^{9} - \frac{161}{8}e^{7} + 57e^{5} - 53e^{3} + 8e$ |
| 31 | $[31, 31, 4w + 33]$ | $\phantom{-}\frac{1}{8}e^{11} - \frac{11}{4}e^{9} + \frac{161}{8}e^{7} - 57e^{5} + 53e^{3} - 8e$ |
| 37 | $[37, 37, w + 12]$ | $\phantom{-}\frac{1}{4}e^{10} - \frac{45}{8}e^{8} + 43e^{6} - \frac{1065}{8}e^{4} + 149e^{2} - 32$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}\frac{1}{4}e^{10} - \frac{45}{8}e^{8} + 43e^{6} - \frac{1065}{8}e^{4} + 149e^{2} - 32$ |
| 53 | $[53, 53, w + 21]$ | $\phantom{-}\frac{1}{4}e^{10} - \frac{11}{2}e^{8} + \frac{163}{4}e^{6} - 122e^{4} + \frac{279}{2}e^{2} - 44$ |
| 53 | $[53, 53, w + 32]$ | $\phantom{-}\frac{1}{4}e^{10} - \frac{11}{2}e^{8} + \frac{163}{4}e^{6} - 122e^{4} + \frac{279}{2}e^{2} - 44$ |
| 61 | $[61, 61, -w - 3]$ | $-\frac{7}{16}e^{11} + \frac{157}{16}e^{9} - \frac{1197}{16}e^{7} + \frac{3723}{16}e^{5} - \frac{1093}{4}e^{3} + 78e$ |
| 61 | $[61, 61, w - 3]$ | $\phantom{-}\frac{7}{16}e^{11} - \frac{157}{16}e^{9} + \frac{1197}{16}e^{7} - \frac{3723}{16}e^{5} + \frac{1093}{4}e^{3} - 78e$ |
| 73 | $[73, 73, w + 17]$ | $\phantom{-}\frac{3}{8}e^{11} - \frac{67}{8}e^{9} + \frac{507}{8}e^{7} - \frac{1557}{8}e^{5} + \frac{901}{4}e^{3} - 68e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $-1$ |