Base field 3.3.1765.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 11x + 16\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w^{2} - 9]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 14x^{8} + 63x^{6} - 110x^{4} + 68x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} - w + 9]$ | $-e^{9} + \frac{25}{2}e^{7} - 44e^{5} + \frac{83}{2}e^{3} + e$ |
| 5 | $[5, 5, -2w^{2} - w + 21]$ | $-2e^{8} + 25e^{6} - 89e^{4} + 91e^{2} - 9$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{3}{2}e^{8} - \frac{37}{2}e^{6} + 64e^{4} - 61e^{2} + 4$ |
| 13 | $[13, 13, -2w^{2} - w + 19]$ | $\phantom{-}e^{9} - 12e^{7} + 38e^{5} - 22e^{3} - 15e$ |
| 13 | $[13, 13, w^{2} - 9]$ | $\phantom{-}1$ |
| 13 | $[13, 13, 3w^{2} + 2w - 29]$ | $\phantom{-}e^{9} - 12e^{7} + 38e^{5} - 22e^{3} - 15e$ |
| 17 | $[17, 17, -w^{2} - 2w + 7]$ | $\phantom{-}\frac{1}{2}e^{9} - 6e^{7} + 19e^{5} - \frac{21}{2}e^{3} - 12e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{2}e^{9} + 6e^{7} - 19e^{5} + \frac{21}{2}e^{3} + 9e$ |
| 27 | $[27, 3, -3]$ | $-2e^{8} + 25e^{6} - 89e^{4} + 92e^{2} - 8$ |
| 31 | $[31, 31, -w^{2} + 7]$ | $\phantom{-}e^{9} - 13e^{7} + \frac{101}{2}e^{5} - \frac{133}{2}e^{3} + 30e$ |
| 43 | $[43, 43, w^{2} - 13]$ | $-\frac{1}{2}e^{8} + \frac{13}{2}e^{6} - 25e^{4} + 30e^{2} - 9$ |
| 47 | $[47, 47, 2w^{2} + 3w - 11]$ | $\phantom{-}\frac{1}{2}e^{9} - \frac{11}{2}e^{7} + 12e^{5} + 18e^{3} - 42e$ |
| 59 | $[59, 59, w^{2} - 5]$ | $-e^{9} + \frac{25}{2}e^{7} - \frac{91}{2}e^{5} + 56e^{3} - 29e$ |
| 61 | $[61, 61, 5w^{2} + 4w - 47]$ | $\phantom{-}3e^{9} - \frac{77}{2}e^{7} + \frac{289}{2}e^{5} - 168e^{3} + 37e$ |
| 61 | $[61, 61, 4w - 7]$ | $-\frac{3}{2}e^{9} + \frac{37}{2}e^{7} - \frac{129}{2}e^{5} + \frac{133}{2}e^{3} - 15e$ |
| 61 | $[61, 61, w - 5]$ | $-\frac{1}{2}e^{8} + 7e^{6} - \frac{61}{2}e^{4} + 44e^{2} - 6$ |
| 71 | $[71, 71, -2w^{2} - 2w + 21]$ | $\phantom{-}3e^{9} - \frac{73}{2}e^{7} + 120e^{5} - \frac{171}{2}e^{3} - 35e$ |
| 73 | $[73, 73, -2w^{2} + 4w - 1]$ | $-\frac{1}{2}e^{9} + \frac{11}{2}e^{7} - 12e^{5} - 17e^{3} + 33e$ |
| 79 | $[79, 79, w + 5]$ | $\phantom{-}\frac{5}{2}e^{8} - 30e^{6} + \frac{197}{2}e^{4} - 83e^{2} - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{2} - 9]$ | $-1$ |