Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w^{2} - 2w - 8]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 64x^{14} + 1674x^{12} - 23264x^{10} + 187400x^{8} - 895688x^{6} + 2481888x^{4} - 3644800x^{2} + 2166784\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}\frac{2468813}{3126308992}e^{14} - \frac{18544069}{390788624}e^{12} + \frac{1776729913}{1563154496}e^{10} - \frac{2723370391}{195394312}e^{8} + \frac{36617989801}{390788624}e^{6} - \frac{134125437461}{390788624}e^{4} + \frac{61699591449}{97697156}e^{2} - \frac{10937189444}{24424289}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $...$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $...$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $\phantom{-}\frac{18347}{48848578}e^{14} - \frac{2051197}{97697156}e^{12} + \frac{22116385}{48848578}e^{10} - \frac{231610591}{48848578}e^{8} + \frac{1215908615}{48848578}e^{6} - \frac{1467057244}{24424289}e^{4} + \frac{1115942476}{24424289}e^{2} + \frac{427799382}{24424289}$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $...$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{684491}{1563154496}e^{14} - \frac{5479209}{195394312}e^{12} + \frac{565438839}{781577248}e^{10} - \frac{942191931}{97697156}e^{8} + \frac{13823512723}{195394312}e^{6} - \frac{54796568419}{195394312}e^{4} + \frac{26585848031}{48848578}e^{2} - \frac{9517102822}{24424289}$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $...$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $...$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $-\frac{2468813}{1563154496}e^{14} + \frac{18544069}{195394312}e^{12} - \frac{1776729913}{781577248}e^{10} + \frac{2723370391}{97697156}e^{8} - \frac{36617989801}{195394312}e^{6} + \frac{134125437461}{195394312}e^{4} - \frac{61699591449}{48848578}e^{2} + \frac{21923227466}{24424289}$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $-\frac{18347}{48848578}e^{14} + \frac{2051197}{97697156}e^{12} - \frac{22116385}{48848578}e^{10} + \frac{231610591}{48848578}e^{8} - \frac{1215908615}{48848578}e^{6} + \frac{1467057244}{24424289}e^{4} - \frac{1115942476}{24424289}e^{2} - \frac{427799382}{24424289}$ |
| 47 | $[47, 47, -2w + 7]$ | $...$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $...$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}\frac{4652129}{1563154496}e^{14} - \frac{34760831}{195394312}e^{12} + \frac{3308055581}{781577248}e^{10} - \frac{5028619831}{97697156}e^{8} + \frac{66973120581}{195394312}e^{6} - \frac{242812022305}{195394312}e^{4} + \frac{110367895885}{48848578}e^{2} - \frac{38523366678}{24424289}$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $...$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $-\frac{118513}{97697156}e^{14} + \frac{13944677}{195394312}e^{12} - \frac{162452007}{97697156}e^{10} + \frac{1924430561}{97697156}e^{8} - \frac{3110973658}{24424289}e^{6} + \frac{11002698991}{24424289}e^{4} - \frac{19869778138}{24424289}e^{2} + \frac{14167421644}{24424289}$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{2} - 2w - 8]$ | $-1$ |