Base field 3.3.1708.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + w + 9]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} + 3x^{13} - 16x^{12} - 49x^{11} + 97x^{10} + 304x^{9} - 276x^{8} - 896x^{7} + 355x^{6} + 1278x^{5} - 122x^{4} - 780x^{3} - 52x^{2} + 116x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w^{2} - 2w - 5]$ | $-\frac{2}{49}e^{13} - \frac{23}{98}e^{12} + \frac{31}{49}e^{11} + \frac{391}{98}e^{10} - \frac{403}{98}e^{9} - \frac{1254}{49}e^{8} + \frac{1459}{98}e^{7} + \frac{3743}{49}e^{6} - \frac{1454}{49}e^{5} - \frac{10267}{98}e^{4} + \frac{47}{2}e^{3} + \frac{2638}{49}e^{2} - \frac{65}{49}e - \frac{80}{49}$ |
| 5 | $[5, 5, w^{2} + 3w + 1]$ | $...$ |
| 7 | $[7, 7, -2w^{2} + 2w + 17]$ | $-\frac{6}{49}e^{13} - \frac{69}{98}e^{12} + \frac{44}{49}e^{11} + \frac{977}{98}e^{10} + \frac{261}{98}e^{9} - \frac{2439}{49}e^{8} - \frac{3561}{98}e^{7} + \frac{5055}{49}e^{6} + \frac{4801}{49}e^{5} - \frac{7673}{98}e^{4} - \frac{187}{2}e^{3} + \frac{515}{49}e^{2} + \frac{1079}{49}e + \frac{5}{49}$ |
| 7 | $[7, 7, -w^{2} + w + 9]$ | $-1$ |
| 13 | $[13, 13, 2w + 1]$ | $-\frac{1}{196}e^{13} - \frac{67}{196}e^{12} - \frac{29}{98}e^{11} + \frac{1041}{196}e^{10} + \frac{769}{196}e^{9} - \frac{2935}{98}e^{8} - \frac{751}{49}e^{7} + \frac{7269}{98}e^{6} + \frac{4173}{196}e^{5} - \frac{7733}{98}e^{4} - 11e^{3} + \frac{3379}{98}e^{2} + \frac{96}{49}e - \frac{255}{49}$ |
| 25 | $[25, 5, -3w^{2} + 5w + 19]$ | $...$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 29 | $[29, 29, w^{2} + w - 1]$ | $...$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $-\frac{29}{98}e^{13} - \frac{81}{98}e^{12} + \frac{188}{49}e^{11} + \frac{1083}{98}e^{10} - \frac{1611}{98}e^{9} - \frac{2501}{49}e^{8} + \frac{1179}{49}e^{7} + \frac{4658}{49}e^{6} - \frac{13}{98}e^{5} - \frac{3169}{49}e^{4} - 14e^{3} + \frac{873}{49}e^{2} - \frac{214}{49}e - \frac{482}{49}$ |
| 37 | $[37, 37, 2w^{2} + 6w + 3]$ | $...$ |
| 41 | $[41, 41, -6w^{2} - 14w - 3]$ | $...$ |
| 53 | $[53, 53, -4w^{2} + 6w + 27]$ | $...$ |
| 59 | $[59, 59, 2w^{2} - 4w - 11]$ | $\phantom{-}\frac{31}{14}e^{13} + \frac{61}{14}e^{12} - \frac{263}{7}e^{11} - \frac{925}{14}e^{10} + \frac{3447}{14}e^{9} + \frac{2596}{7}e^{8} - \frac{5483}{7}e^{7} - \frac{6666}{7}e^{6} + \frac{17203}{14}e^{5} + \frac{7820}{7}e^{4} - 815e^{3} - \frac{3473}{7}e^{2} + \frac{936}{7}e - \frac{10}{7}$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $...$ |
| 61 | $[61, 61, -2w^{2} + 2w + 13]$ | $...$ |
| 73 | $[73, 73, w^{2} + 3w + 3]$ | $...$ |
| 97 | $[97, 97, w^{2} + w - 15]$ | $...$ |
| 101 | $[101, 101, w^{2} + 3w - 1]$ | $...$ |
| 101 | $[101, 101, w^{2} - w - 11]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + w + 9]$ | $1$ |