Base field \(\Q(\sqrt{21}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[37,37,-w + 7]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 21x^{6} + 143x^{4} - 376x^{2} + 300\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{1}{2}e^{6} + \frac{17}{2}e^{4} - \frac{75}{2}e^{2} + 40$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{9}{10}e^{7} - \frac{149}{10}e^{5} + \frac{627}{10}e^{3} - \frac{312}{5}e$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{1}{5}e^{7} + \frac{16}{5}e^{5} - \frac{63}{5}e^{3} + \frac{56}{5}e$ |
| 7 | $[7, 7, -w - 3]$ | $-2e^{6} + 33e^{4} - 138e^{2} + 136$ |
| 17 | $[17, 17, -2w + 3]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{17}{2}e^{5} + \frac{75}{2}e^{3} - 40e$ |
| 17 | $[17, 17, -2w - 1]$ | $\phantom{-}\frac{3}{5}e^{7} - \frac{48}{5}e^{5} + \frac{184}{5}e^{3} - \frac{138}{5}e$ |
| 37 | $[37, 37, w + 6]$ | $-4e^{6} + 66e^{4} - 274e^{2} + 262$ |
| 37 | $[37, 37, -w + 7]$ | $-1$ |
| 41 | $[41, 41, 3w + 1]$ | $\phantom{-}2e^{7} - 33e^{5} + 137e^{3} - 130e$ |
| 41 | $[41, 41, -3w + 4]$ | $\phantom{-}\frac{9}{5}e^{7} - \frac{149}{5}e^{5} + \frac{627}{5}e^{3} - \frac{634}{5}e$ |
| 43 | $[43, 43, 3w + 8]$ | $-e^{6} + 17e^{4} - 75e^{2} + 76$ |
| 43 | $[43, 43, 3w - 11]$ | $\phantom{-}e^{6} - 17e^{4} + 76e^{2} - 80$ |
| 47 | $[47, 47, 3w - 2]$ | $-\frac{6}{5}e^{7} + \frac{101}{5}e^{5} - \frac{443}{5}e^{3} + \frac{491}{5}e$ |
| 47 | $[47, 47, 3w - 1]$ | $-\frac{2}{5}e^{7} + \frac{32}{5}e^{5} - \frac{121}{5}e^{3} + \frac{77}{5}e$ |
| 59 | $[59, 59, -5w - 6]$ | $-\frac{7}{5}e^{7} + \frac{117}{5}e^{5} - \frac{501}{5}e^{3} + \frac{522}{5}e$ |
| 59 | $[59, 59, -4w - 3]$ | $\phantom{-}\frac{3}{5}e^{7} - \frac{48}{5}e^{5} + \frac{184}{5}e^{3} - \frac{133}{5}e$ |
| 67 | $[67, 67, -w - 8]$ | $-e^{6} + 17e^{4} - 73e^{2} + 68$ |
| 67 | $[67, 67, w - 9]$ | $-5e^{6} + 83e^{4} - 351e^{2} + 356$ |
| 79 | $[79, 79, 2w - 11]$ | $\phantom{-}3e^{6} - 49e^{4} + 198e^{2} - 172$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37,37,-w + 7]$ | $1$ |