Base field 6.6.703493.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 3x^{2} - 6x - 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ | $\phantom{-}\frac{4}{3}e^{2} + \frac{2}{3}e - \frac{29}{3}$ |
| 13 | $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ | $-\frac{4}{3}e^{2} - \frac{5}{3}e + \frac{26}{3}$ |
| 13 | $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e^{2} + e - 9$ |
| 41 | $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ | $\phantom{-}\frac{5}{3}e^{2} - \frac{2}{3}e - \frac{46}{3}$ |
| 41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $\phantom{-}\frac{5}{3}e^{2} + \frac{7}{3}e - \frac{31}{3}$ |
| 41 | $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ | $-\frac{5}{3}e^{2} - \frac{4}{3}e + \frac{16}{3}$ |
| 43 | $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ | $-\frac{5}{3}e^{2} + \frac{2}{3}e + \frac{28}{3}$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ | $-\frac{7}{3}e^{2} - \frac{8}{3}e + \frac{38}{3}$ |
| 49 | $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ | $-\frac{8}{3}e^{2} - \frac{1}{3}e + \frac{58}{3}$ |
| 64 | $[64, 2, -2]$ | $-4e^{2} - 3e + 18$ |
| 71 | $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ | $-\frac{2}{3}e^{2} - \frac{13}{3}e + \frac{7}{3}$ |
| 71 | $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ | $-\frac{5}{3}e^{2} - \frac{4}{3}e + \frac{7}{3}$ |
| 83 | $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ | $\phantom{-}4e^{2} - e - 35$ |
| 83 | $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ | $-e^{2} + 2e + 1$ |
| 97 | $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ | $-\frac{11}{3}e^{2} - \frac{4}{3}e + \frac{76}{3}$ |
| 97 | $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ | $\phantom{-}\frac{5}{3}e^{2} - \frac{2}{3}e - \frac{55}{3}$ |
| 113 | $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ | $\phantom{-}\frac{11}{3}e^{2} + \frac{13}{3}e - \frac{73}{3}$ |
| 113 | $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ | $\phantom{-}\frac{10}{3}e^{2} - \frac{1}{3}e - \frac{68}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ | $-1$ |