Base field 4.4.18688.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[34,34,\frac{2}{3}w^{3} - \frac{2}{3}w^{2} - 5w + \frac{10}{3}]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 10x^{8} + 2x^{7} - 212x^{6} - 275x^{5} + 1532x^{4} + 1645x^{3} - 4515x^{2} - 2543x + 4557\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ | $...$ |
| 9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ | $-\frac{143566}{113335571}e^{8} + \frac{4257268}{113335571}e^{7} + \frac{36633283}{113335571}e^{6} - \frac{42934116}{113335571}e^{5} - \frac{596552098}{113335571}e^{4} + \frac{3061049}{113335571}e^{3} + \frac{2400824632}{113335571}e^{2} + \frac{357440122}{113335571}e - \frac{2634710633}{113335571}$ |
| 9 | $[9, 3, w + 1]$ | $-\frac{124498}{113335571}e^{8} - \frac{2532050}{113335571}e^{7} - \frac{9941080}{113335571}e^{6} + \frac{28398468}{113335571}e^{5} + \frac{167968549}{113335571}e^{4} - \frac{1227936}{113335571}e^{3} - \frac{444232215}{113335571}e^{2} - \frac{238704904}{113335571}e - \frac{99706412}{113335571}$ |
| 17 | $[17, 17, w + 3]$ | $-1$ |
| 17 | $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ | $-\frac{925149}{113335571}e^{8} - \frac{8994999}{113335571}e^{7} - \frac{10474581}{113335571}e^{6} + \frac{127136672}{113335571}e^{5} + \frac{347552100}{113335571}e^{4} - \frac{326789972}{113335571}e^{3} - \frac{1614743993}{113335571}e^{2} - \frac{39507517}{113335571}e + \frac{1554594573}{113335571}$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ | $-\frac{882424}{113335571}e^{8} - \frac{7410527}{113335571}e^{7} - \frac{111659}{113335571}e^{6} + \frac{116573451}{113335571}e^{5} + \frac{161098506}{113335571}e^{4} - \frac{388972687}{113335571}e^{3} - \frac{719390701}{113335571}e^{2} + \frac{119289058}{113335571}e + \frac{937308258}{113335571}$ |
| 31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ | $...$ |
| 41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ | $...$ |
| 41 | $[41, 41, w^{2} - 5]$ | $...$ |
| 41 | $[41, 41, 2w + 3]$ | $...$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ | $...$ |
| 47 | $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ | $...$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ | $-\frac{515664}{113335571}e^{8} - \frac{4406540}{113335571}e^{7} + \frac{4636558}{113335571}e^{6} + \frac{104044463}{113335571}e^{5} + \frac{52315317}{113335571}e^{4} - \frac{709884401}{113335571}e^{3} - \frac{295582296}{113335571}e^{2} + \frac{879344992}{113335571}e - \frac{58497453}{113335571}$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ | $...$ |
| 73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ | $...$ |
| 73 | $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ | $...$ |
| 73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ | $...$ |
| 103 | $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{8}{3}]$ | $-1$ |
| $17$ | $[17,17,-w - 3]$ | $1$ |