Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,9w + 61]$ |
| Dimension: | $9$ |
| 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:
| \(x^{9} - 11x^{7} + x^{6} + 37x^{5} - 4x^{4} - 42x^{3} + 4x^{2} + 12x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 7]$ | $-2e^{8} - \frac{1}{2}e^{7} + \frac{43}{2}e^{6} + \frac{7}{2}e^{5} - \frac{139}{2}e^{4} - \frac{21}{2}e^{3} + 72e^{2} + \frac{25}{2}e - \frac{29}{2}$ |
| 3 | $[3, 3, w - 7]$ | $\phantom{-}\frac{3}{2}e^{8} - 16e^{6} + e^{5} + 50e^{4} - \frac{3}{2}e^{3} - \frac{93}{2}e^{2} - 4e + \frac{13}{2}$ |
| 5 | $[5, 5, -9w + 61]$ | $-\frac{3}{2}e^{8} - \frac{1}{2}e^{7} + \frac{33}{2}e^{6} + \frac{9}{2}e^{5} - \frac{111}{2}e^{4} - 16e^{3} + \frac{123}{2}e^{2} + \frac{39}{2}e - 15$ |
| 5 | $[5, 5, -9w - 61]$ | $\phantom{-}1$ |
| 7 | $[7, 7, 4w - 27]$ | $\phantom{-}e^{8} + \frac{1}{2}e^{7} - \frac{23}{2}e^{6} - \frac{9}{2}e^{5} + \frac{83}{2}e^{4} + \frac{27}{2}e^{3} - 51e^{2} - \frac{27}{2}e + \frac{27}{2}$ |
| 7 | $[7, 7, 4w + 27]$ | $\phantom{-}\frac{3}{2}e^{8} + e^{7} - 16e^{6} - 9e^{5} + 52e^{4} + \frac{53}{2}e^{3} - \frac{113}{2}e^{2} - 24e + \frac{27}{2}$ |
| 23 | $[23, 23, 78w - 529]$ | $-3e^{8} - \frac{3}{2}e^{7} + \frac{65}{2}e^{6} + \frac{27}{2}e^{5} - \frac{213}{2}e^{4} - \frac{85}{2}e^{3} + 112e^{2} + \frac{87}{2}e - \frac{51}{2}$ |
| 37 | $[37, 37, -w - 3]$ | $-2e^{8} - 2e^{7} + 22e^{6} + 19e^{5} - 76e^{4} - 56e^{3} + 90e^{2} + 48e - 24$ |
| 37 | $[37, 37, w - 3]$ | $-\frac{11}{2}e^{8} - \frac{5}{2}e^{7} + \frac{117}{2}e^{6} + \frac{39}{2}e^{5} - \frac{375}{2}e^{4} - 52e^{3} + \frac{381}{2}e^{2} + \frac{99}{2}e - 36$ |
| 41 | $[41, 41, -2w + 15]$ | $-\frac{3}{2}e^{8} - \frac{1}{2}e^{7} + \frac{35}{2}e^{6} + \frac{11}{2}e^{5} - \frac{129}{2}e^{4} - 23e^{3} + \frac{165}{2}e^{2} + \frac{55}{2}e - 21$ |
| 41 | $[41, 41, 2w + 15]$ | $-\frac{11}{2}e^{8} - 2e^{7} + 60e^{6} + 16e^{5} - 199e^{4} - \frac{95}{2}e^{3} + \frac{427}{2}e^{2} + 50e - \frac{87}{2}$ |
| 53 | $[53, 53, -3w - 19]$ | $\phantom{-}2e^{8} - 21e^{6} + 2e^{5} + 64e^{4} - 8e^{3} - 59e^{2} + 9e + 9$ |
| 53 | $[53, 53, 3w - 19]$ | $\phantom{-}\frac{7}{2}e^{8} - 37e^{6} + 3e^{5} + 116e^{4} - \frac{13}{2}e^{3} - \frac{233}{2}e^{2} - 9e + \frac{45}{2}$ |
| 59 | $[59, 59, 11w - 75]$ | $\phantom{-}\frac{3}{2}e^{8} + e^{7} - 16e^{6} - 9e^{5} + 52e^{4} + \frac{55}{2}e^{3} - \frac{105}{2}e^{2} - 27e + \frac{9}{2}$ |
| 59 | $[59, 59, -11w - 75]$ | $-4e^{8} - \frac{5}{2}e^{7} + \frac{89}{2}e^{6} + \frac{45}{2}e^{5} - \frac{309}{2}e^{4} - \frac{133}{2}e^{3} + 182e^{2} + \frac{135}{2}e - \frac{93}{2}$ |
| 61 | $[61, 61, -5w + 33]$ | $-\frac{11}{2}e^{8} - \frac{3}{2}e^{7} + \frac{117}{2}e^{6} + \frac{21}{2}e^{5} - \frac{373}{2}e^{4} - 33e^{3} + \frac{383}{2}e^{2} + \frac{87}{2}e - 45$ |
| 61 | $[61, 61, 5w + 33]$ | $\phantom{-}9e^{8} + 4e^{7} - 99e^{6} - 35e^{5} + 334e^{4} + 108e^{3} - 371e^{2} - 108e + 84$ |
| 73 | $[73, 73, -24w - 163]$ | $\phantom{-}\frac{5}{2}e^{8} + 2e^{7} - 28e^{6} - 19e^{5} + 99e^{4} + \frac{115}{2}e^{3} - \frac{245}{2}e^{2} - 54e + \frac{77}{2}$ |
| 73 | $[73, 73, -24w + 163]$ | $\phantom{-}7e^{8} + \frac{3}{2}e^{7} - \frac{153}{2}e^{6} - \frac{21}{2}e^{5} + \frac{505}{2}e^{4} + \frac{71}{2}e^{3} - 265e^{2} - \frac{105}{2}e + \frac{95}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,9w + 61]$ | $-1$ |