Base field \(\Q(\sqrt{123}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 123\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $76$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 24x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 11]$ | $-\frac{1}{8}e^{2} - \frac{3}{2}$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{16}e^{3} - \frac{5}{4}e$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{1}{4}e^{3} - 6e$ |
| 17 | $[17, 17, w + 2]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{11}{2}e$ |
| 17 | $[17, 17, w + 15]$ | $-\frac{1}{8}e^{3} - 2e$ |
| 19 | $[19, 19, w + 3]$ | $-\frac{1}{8}e^{3} - \frac{5}{2}e$ |
| 19 | $[19, 19, w + 16]$ | $-\frac{1}{8}e^{3} - \frac{5}{2}e$ |
| 23 | $[23, 23, -w - 10]$ | $\phantom{-}\frac{1}{4}e^{2} + 5$ |
| 23 | $[23, 23, w - 10]$ | $\phantom{-}\frac{1}{4}e^{2} + 1$ |
| 25 | $[25, 5, -5]$ | $-2$ |
| 29 | $[29, 29, w + 6]$ | $-\frac{3}{8}e^{3} - 9e$ |
| 29 | $[29, 29, w + 23]$ | $-\frac{3}{2}e$ |
| 37 | $[37, 37, 9w + 100]$ | $-\frac{1}{2}e^{2} - 9$ |
| 37 | $[37, 37, -2w - 23]$ | $\phantom{-}\frac{1}{2}e^{2} + 3$ |
| 41 | $[41, 41, w]$ | $-\frac{1}{8}e^{3} - \frac{7}{2}e$ |
| 53 | $[53, 53, w + 21]$ | $\phantom{-}\frac{5}{8}e^{3} + \frac{27}{2}e$ |
| 53 | $[53, 53, w + 32]$ | $-\frac{3}{8}e^{3} - \frac{13}{2}e$ |
| 59 | $[59, 59, -w - 8]$ | $-\frac{1}{4}e^{2} + 1$ |
| 59 | $[59, 59, w - 8]$ | $-\frac{1}{4}e^{2} - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $\frac{1}{16}e^{3} + \frac{5}{4}e$ |