Base field \(\Q(\sqrt{82}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 82\); narrow class number \(4\) and class number \(4\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3,3,-w + 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 2x^{6} - 7x^{5} + 12x^{4} + 15x^{3} - 16x^{2} - 12x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-e^{5} + e^{4} + 6e^{3} - 4e^{2} - 7e + 1$ |
| 3 | $[3, 3, w + 2]$ | $-1$ |
| 11 | $[11, 11, w + 4]$ | $\phantom{-}e^{6} - e^{5} - 6e^{4} + 6e^{3} + 8e^{2} - 10e - 2$ |
| 11 | $[11, 11, w + 7]$ | $-e^{6} - 2e^{5} + 8e^{4} + 13e^{3} - 15e^{2} - 17e + 2$ |
| 13 | $[13, 13, w + 2]$ | $-e^{6} + 3e^{5} + 5e^{4} - 17e^{3} - 4e^{2} + 19e + 3$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}3e^{6} - 2e^{5} - 19e^{4} + 8e^{3} + 28e^{2} - 3e - 7$ |
| 19 | $[19, 19, w + 5]$ | $-e^{6} + 2e^{5} + 4e^{4} - 8e^{3} + e^{2} + 3e - 5$ |
| 19 | $[19, 19, w + 14]$ | $-2e^{6} - e^{5} + 13e^{4} + 9e^{3} - 19e^{2} - 16e + 4$ |
| 23 | $[23, 23, w + 6]$ | $-e^{5} + e^{4} + 6e^{3} - 2e^{2} - 6e - 6$ |
| 23 | $[23, 23, w + 17]$ | $\phantom{-}e^{6} - 3e^{5} - 4e^{4} + 16e^{3} + e^{2} - 18e - 1$ |
| 25 | $[25, 5, -5]$ | $-2e^{6} + 14e^{4} + 2e^{3} - 24e^{2} - 5e + 1$ |
| 29 | $[29, 29, w + 13]$ | $\phantom{-}2e^{5} - 15e^{3} + 26e + 3$ |
| 29 | $[29, 29, w + 16]$ | $\phantom{-}e^{6} - 5e^{4} - e^{3} + 5e + 8$ |
| 31 | $[31, 31, w + 12]$ | $\phantom{-}2e^{6} + 2e^{5} - 16e^{4} - 15e^{3} + 31e^{2} + 25e - 5$ |
| 31 | $[31, 31, w + 19]$ | $-2e^{5} + 4e^{4} + 12e^{3} - 20e^{2} - 14e + 12$ |
| 41 | $[41, 41, w]$ | $\phantom{-}e^{6} - 3e^{5} - 4e^{4} + 18e^{3} + 2e^{2} - 26e - 6$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e^{6} - e^{5} - 13e^{4} + 4e^{3} + 18e^{2} - 4$ |
| 53 | $[53, 53, w + 20]$ | $\phantom{-}e^{6} - 2e^{5} - 4e^{4} + 12e^{3} - 2e^{2} - 16e + 3$ |
| 53 | $[53, 53, w + 33]$ | $\phantom{-}6e^{6} - e^{5} - 39e^{4} - 3e^{3} + 57e^{2} + 22e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $1$ |