Base field \(\Q(\sqrt{93}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 23\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[21, 21, w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 3x^{2} - x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 5]$ | $\phantom{-}1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 6]$ | $-1$ |
| 7 | $[7, 7, -w - 5]$ | $\phantom{-}e^{2} - 2e - 3$ |
| 11 | $[11, 11, -w - 3]$ | $-2$ |
| 11 | $[11, 11, w - 4]$ | $-3e^{2} + 3e + 8$ |
| 17 | $[17, 17, w + 2]$ | $-2e - 2$ |
| 17 | $[17, 17, w - 3]$ | $\phantom{-}e - 3$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}3e^{2} - 4e - 5$ |
| 19 | $[19, 19, -w + 7]$ | $-e^{2} + 2e + 1$ |
| 23 | $[23, 23, w]$ | $-2e^{2} + 2e + 4$ |
| 23 | $[23, 23, w - 1]$ | $\phantom{-}e^{2} - e - 8$ |
| 25 | $[25, 5, -5]$ | $-e^{2} - 2e + 7$ |
| 29 | $[29, 29, -2w + 9]$ | $\phantom{-}4e - 4$ |
| 29 | $[29, 29, 2w + 7]$ | $\phantom{-}2e^{2} - 6e - 2$ |
| 31 | $[31, 31, 3w - 17]$ | $\phantom{-}e^{2} - 2e - 5$ |
| 53 | $[53, 53, 3w - 14]$ | $\phantom{-}5e^{2} - 7e - 10$ |
| 53 | $[53, 53, -3w - 11]$ | $-2e^{2} + 3e - 1$ |
| 67 | $[67, 67, -w - 9]$ | $-7e^{2} + 10e + 11$ |
| 67 | $[67, 67, w - 10]$ | $\phantom{-}5e^{2} - 4e - 19$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 5]$ | $-1$ |
| $7$ | $[7, 7, w - 6]$ | $1$ |