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: | $[6, 6, w + 3]$ |
| Dimension: | $16$ |
| 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:
| \(x^{16} + 74x^{14} + 2185x^{12} + 33232x^{10} + 281740x^{8} + 1343872x^{6} + 3439972x^{4} + 4172272x^{2} + 1827904\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 11]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, w + 15]$ | $...$ |
| 19 | $[19, 19, w + 3]$ | $...$ |
| 19 | $[19, 19, w + 16]$ | $...$ |
| 23 | $[23, 23, -w - 10]$ | $...$ |
| 23 | $[23, 23, w - 10]$ | $...$ |
| 25 | $[25, 5, -5]$ | $-\frac{1132565}{53202885944}e^{14} - \frac{35712407}{26601442972}e^{12} - \frac{1669864695}{53202885944}e^{10} - \frac{9087339843}{26601442972}e^{8} - \frac{25235761309}{13300721486}e^{6} - \frac{42871820098}{6650360743}e^{4} - \frac{205887777323}{13300721486}e^{2} - \frac{411961699}{39351247}$ |
| 29 | $[29, 29, w + 6]$ | $...$ |
| 29 | $[29, 29, w + 23]$ | $...$ |
| 37 | $[37, 37, 9w + 100]$ | $...$ |
| 37 | $[37, 37, -2w - 23]$ | $...$ |
| 41 | $[41, 41, w]$ | $...$ |
| 53 | $[53, 53, w + 21]$ | $\phantom{-}\frac{621667}{26541394568}e^{15} + \frac{19525011}{13270697284}e^{13} + \frac{890978303}{26541394568}e^{11} + \frac{1080501211}{3317674321}e^{9} + \frac{3287204203}{3317674321}e^{7} - \frac{11333974016}{3317674321}e^{5} - \frac{149037221643}{6635348642}e^{3} - \frac{420654847}{19631209}e$ |
| 53 | $[53, 53, w + 32]$ | $...$ |
| 59 | $[59, 59, -w - 8]$ | $...$ |
| 59 | $[59, 59, w - 8]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 11]$ | $-1$ |
| $3$ | $[3, 3, w]$ | $-\frac{621667}{106165578272}e^{15} - \frac{19525011}{53082789136}e^{13} - \frac{890978303}{106165578272}e^{11} - \frac{1080501211}{13270697284}e^{9} - \frac{3287204203}{13270697284}e^{7} + \frac{2833493504}{3317674321}e^{5} + \frac{149037221643}{26541394568}e^{3} + \frac{110071514}{19631209}e$ |