Base field 3.3.1772.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x + 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 2x^{9} - 14x^{8} - 25x^{7} + 66x^{6} + 100x^{5} - 114x^{4} - 136x^{3} + 40x^{2} + 32x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w^{2} + 11]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{2}e^{7} - 3e^{6} - \frac{21}{4}e^{5} + \frac{23}{2}e^{4} + \frac{31}{2}e^{3} - \frac{31}{2}e^{2} - 11e + 4$ |
| 3 | $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ | $\phantom{-}\frac{1}{4}e^{9} + \frac{1}{2}e^{8} - \frac{7}{2}e^{7} - \frac{27}{4}e^{6} + \frac{31}{2}e^{5} + 30e^{4} - 20e^{3} - 46e^{2} - 6e + 8$ |
| 9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{5}{2}w - 1]$ | $-\frac{1}{4}e^{9} - \frac{1}{2}e^{8} + \frac{7}{2}e^{7} + \frac{23}{4}e^{6} - \frac{33}{2}e^{5} - 19e^{4} + 28e^{3} + 15e^{2} - 6e + 2$ |
| 25 | $[25, 5, \frac{7}{2}w^{2} - \frac{31}{2}w + 9]$ | $\phantom{-}\frac{1}{4}e^{9} + \frac{1}{2}e^{8} - 4e^{7} - \frac{27}{4}e^{6} + \frac{43}{2}e^{5} + \frac{57}{2}e^{4} - 41e^{3} - 38e^{2} + 13e + 6$ |
| 29 | $[29, 29, -\frac{5}{2}w^{2} + \frac{1}{2}w + 29]$ | $-\frac{1}{4}e^{9} + \frac{9}{2}e^{7} - \frac{1}{4}e^{6} - 27e^{5} + 3e^{4} + 58e^{3} - 10e^{2} - 26e + 10$ |
| 41 | $[41, 41, -w^{2} + 3w - 1]$ | $-\frac{3}{4}e^{9} - \frac{3}{2}e^{8} + 10e^{7} + \frac{69}{4}e^{6} - \frac{89}{2}e^{5} - \frac{119}{2}e^{4} + 70e^{3} + 58e^{2} - 11e - 2$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - \frac{3}{2}w + 3]$ | $-\frac{1}{4}e^{9} - \frac{1}{2}e^{8} + 3e^{7} + \frac{19}{4}e^{6} - \frac{25}{2}e^{5} - \frac{21}{2}e^{4} + 25e^{3} - 23e - 2$ |
| 41 | $[41, 41, 2w + 7]$ | $\phantom{-}\frac{1}{4}e^{9} + \frac{1}{2}e^{8} - \frac{7}{2}e^{7} - \frac{23}{4}e^{6} + \frac{35}{2}e^{5} + 20e^{4} - 36e^{3} - 19e^{2} + 20e - 2$ |
| 43 | $[43, 43, -\frac{7}{2}w^{2} - \frac{1}{2}w + 37]$ | $\phantom{-}e^{9} + 2e^{8} - 13e^{7} - 23e^{6} + 55e^{5} + 81e^{4} - 79e^{3} - 90e^{2} + 10e + 12$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{9}{2}w + 3]$ | $\phantom{-}\frac{1}{2}e^{9} + e^{8} - 7e^{7} - \frac{25}{2}e^{6} + 32e^{5} + 50e^{4} - 46e^{3} - 68e^{2} - 10e + 12$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{1}{2}w + 1]$ | $-\frac{1}{2}e^{9} - e^{8} + \frac{13}{2}e^{7} + \frac{25}{2}e^{6} - 27e^{5} - \frac{101}{2}e^{4} + 37e^{3} + 70e^{2} - 5e - 14$ |
| 47 | $[47, 47, -w^{2} + w + 15]$ | $\phantom{-}e^{9} + \frac{3}{2}e^{8} - 14e^{7} - 17e^{6} + \frac{131}{2}e^{5} + 57e^{4} - 111e^{3} - 53e^{2} + 34e$ |
| 53 | $[53, 53, -2w^{2} + 2w + 29]$ | $-\frac{3}{4}e^{9} - 2e^{8} + \frac{19}{2}e^{7} + \frac{97}{4}e^{6} - 39e^{5} - 92e^{4} + 54e^{3} + 114e^{2} - 2e - 18$ |
| 59 | $[59, 59, w^{2} - w - 13]$ | $-e^{9} - 2e^{8} + \frac{27}{2}e^{7} + 24e^{6} - 60e^{5} - \frac{179}{2}e^{4} + 92e^{3} + 104e^{2} - 15e - 10$ |
| 67 | $[67, 67, -\frac{1}{2}w^{2} + \frac{1}{2}w + 9]$ | $\phantom{-}\frac{1}{2}e^{9} + e^{8} - \frac{13}{2}e^{7} - \frac{23}{2}e^{6} + 28e^{5} + \frac{83}{2}e^{4} - 44e^{3} - 52e^{2} + 13e + 10$ |
| 71 | $[71, 71, 2w - 3]$ | $-e^{6} - 2e^{5} + 9e^{4} + 16e^{3} - 18e^{2} - 28e$ |
| 73 | $[73, 73, \frac{3}{2}w^{2} - \frac{11}{2}w + 1]$ | $-\frac{1}{2}e^{9} - e^{8} + 7e^{7} + \frac{27}{2}e^{6} - 31e^{5} - 59e^{4} + 39e^{3} + 86e^{2} + 18e - 10$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} + \frac{15}{2}w - 5]$ | $-\frac{3}{2}e^{9} - 3e^{8} + 21e^{7} + \frac{73}{2}e^{6} - 98e^{5} - 137e^{4} + 158e^{3} + 158e^{2} - 18e - 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ | $-1$ |