Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, -2w + 1]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} + 3x^{14} - 24x^{13} - 85x^{12} + 194x^{11} + 932x^{10} - 370x^{9} - 4839x^{8} - 2849x^{7} + 11003x^{6} + 15300x^{5} - 3785x^{4} - 20034x^{3} - 14946x^{2} - 4322x - 379\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $...$ |
| 5 | $[5, 5, w - 1]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $...$ |
| 13 | $[13, 13, -2w + 1]$ | $\phantom{-}1$ |
| 19 | $[19, 19, 2w^{2} - w - 15]$ | $...$ |
| 25 | $[25, 5, w^{2} - 7]$ | $...$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 31 | $[31, 31, w^{2} - 2w - 1]$ | $...$ |
| 37 | $[37, 37, -3w^{2} + 2w + 23]$ | $...$ |
| 41 | $[41, 41, -2w - 1]$ | $...$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{3}{2}e^{14} - \frac{7}{2}e^{13} + 38e^{12} + 101e^{11} - 352e^{10} - \frac{2273}{2}e^{9} + \frac{2561}{2}e^{8} + \frac{12367}{2}e^{7} + \frac{195}{2}e^{6} - 15830e^{5} - 11598e^{4} + \frac{25617}{2}e^{3} + 20013e^{2} + 8147e + \frac{1649}{2}$ |
| 49 | $[49, 7, w^{2} - 2w - 5]$ | $-\frac{17}{4}e^{14} - \frac{31}{4}e^{13} + \frac{437}{4}e^{12} + \frac{461}{2}e^{11} - \frac{4203}{4}e^{10} - 2663e^{9} + \frac{17183}{4}e^{8} + \frac{59447}{4}e^{7} - \frac{7341}{2}e^{6} - 39227e^{5} - \frac{43445}{2}e^{4} + \frac{136901}{4}e^{3} + 44786e^{2} + \frac{67953}{4}e + 1680$ |
| 59 | $[59, 59, 2w - 3]$ | $...$ |
| 67 | $[67, 67, w - 5]$ | $\phantom{-}\frac{1}{4}e^{14} + \frac{5}{4}e^{13} - \frac{25}{4}e^{12} - \frac{67}{2}e^{11} + \frac{211}{4}e^{10} + 352e^{9} - \frac{469}{4}e^{8} - \frac{7175}{4}e^{7} - 664e^{6} + 4292e^{5} + \frac{7789}{2}e^{4} - \frac{12509}{4}e^{3} - \frac{11033}{2}e^{2} - \frac{9167}{4}e - \frac{463}{2}$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $...$ |
| 73 | $[73, 73, w^{2} + 1]$ | $...$ |
| 83 | $[83, 83, -4w^{2} + 3w + 27]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -2w + 1]$ | $-1$ |