Base field 6.6.1202933.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 6x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[35, 35, 2w^{5} - 11w^{3} - 4w^{2} + 7w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 14x^{4} + 58x^{3} - 60x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{14}e^{4} - \frac{5}{7}e^{3} + \frac{9}{7}e^{2} + \frac{13}{7}e + \frac{3}{7}$ |
| 25 | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $\phantom{-}\frac{2}{7}e^{4} - \frac{20}{7}e^{3} + \frac{50}{7}e^{2} - \frac{11}{7}e - \frac{30}{7}$ |
| 41 | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $-\frac{5}{14}e^{4} + \frac{32}{7}e^{3} - \frac{122}{7}e^{2} + \frac{131}{7}e - \frac{29}{7}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{3}{7}e^{4} - \frac{37}{7}e^{3} + \frac{138}{7}e^{2} - \frac{153}{7}e + \frac{32}{7}$ |
| 53 | $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ | $\phantom{-}\frac{4}{7}e^{4} - \frac{40}{7}e^{3} + \frac{100}{7}e^{2} - \frac{43}{7}e - \frac{4}{7}$ |
| 59 | $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ | $-\frac{2}{7}e^{4} + \frac{13}{7}e^{3} + \frac{13}{7}e^{2} - \frac{108}{7}e + \frac{44}{7}$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}\frac{2}{7}e^{4} - \frac{34}{7}e^{3} + \frac{148}{7}e^{2} - \frac{67}{7}e - \frac{72}{7}$ |
| 64 | $[64, 2, -2]$ | $-\frac{3}{14}e^{4} + \frac{22}{7}e^{3} - \frac{83}{7}e^{2} + \frac{24}{7}e + \frac{47}{7}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + w - 3]$ | $\phantom{-}\frac{9}{14}e^{4} - \frac{66}{7}e^{3} + \frac{277}{7}e^{2} - \frac{247}{7}e - \frac{15}{7}$ |
| 67 | $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ | $-\frac{1}{7}e^{4} + \frac{10}{7}e^{3} - \frac{25}{7}e^{2} + \frac{9}{7}e + \frac{8}{7}$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ | $-\frac{6}{7}e^{4} + \frac{67}{7}e^{3} - \frac{199}{7}e^{2} + \frac{75}{7}e + \frac{76}{7}$ |
| 73 | $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ | $-\frac{6}{7}e^{4} + \frac{81}{7}e^{3} - \frac{311}{7}e^{2} + \frac{236}{7}e + \frac{27}{7}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{7}e^{4} - \frac{17}{7}e^{3} + \frac{88}{7}e^{2} - \frac{135}{7}e + \frac{13}{7}$ |
| 83 | $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ | $-e^{4} + 13e^{3} - 48e^{2} + 36e + 8$ |
| 89 | $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ | $\phantom{-}\frac{5}{7}e^{4} - \frac{78}{7}e^{3} + \frac{335}{7}e^{2} - \frac{276}{7}e - \frac{19}{7}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{1}{7}e^{4} + \frac{17}{7}e^{3} - \frac{88}{7}e^{2} + \frac{100}{7}e + \frac{106}{7}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $-\frac{1}{7}e^{4} + \frac{17}{7}e^{3} - \frac{60}{7}e^{2} - \frac{40}{7}e + \frac{22}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $-1$ |
| $7$ | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $-1$ |