Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{3} + 4w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 6x^{6} - 6x^{5} - 88x^{4} - 114x^{3} + 88x^{2} + 152x + 40\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $-1$ |
| 5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-1$ |
| 7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{71}e^{6} + \frac{37}{142}e^{5} + \frac{30}{71}e^{4} - \frac{281}{71}e^{3} - \frac{609}{71}e^{2} + \frac{392}{71}e + \frac{508}{71}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $-\frac{5}{142}e^{6} - \frac{57}{142}e^{5} - \frac{4}{71}e^{4} + \frac{454}{71}e^{3} + \frac{564}{71}e^{2} - \frac{909}{71}e - \frac{702}{71}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{6}{71}e^{6} - \frac{40}{71}e^{5} + \frac{33}{71}e^{4} + \frac{621}{71}e^{3} + \frac{743}{71}e^{2} - \frac{1074}{71}e - \frac{1060}{71}$ |
| 32 | $[32, 2, 2]$ | $-\frac{49}{142}e^{6} - \frac{116}{71}e^{5} + \frac{259}{71}e^{4} + \frac{1737}{71}e^{3} + \frac{1111}{71}e^{2} - \frac{2362}{71}e - \frac{1583}{71}$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $-\frac{5}{142}e^{6} - \frac{57}{142}e^{5} - \frac{4}{71}e^{4} + \frac{454}{71}e^{3} + \frac{564}{71}e^{2} - \frac{909}{71}e - \frac{844}{71}$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{71}e^{6} + \frac{37}{142}e^{5} + \frac{30}{71}e^{4} - \frac{281}{71}e^{3} - \frac{680}{71}e^{2} + \frac{321}{71}e + \frac{792}{71}$ |
| 43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $-\frac{2}{71}e^{6} - \frac{3}{142}e^{5} + \frac{11}{71}e^{4} - \frac{6}{71}e^{3} + \frac{224}{71}e^{2} + \frac{281}{71}e - \frac{306}{71}$ |
| 43 | $[43, 43, -w^{2} + w + 3]$ | $-\frac{3}{142}e^{6} - \frac{10}{71}e^{5} + \frac{26}{71}e^{4} + \frac{173}{71}e^{3} - \frac{116}{71}e^{2} - \frac{446}{71}e + \frac{232}{71}$ |
| 47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $\phantom{-}\frac{16}{71}e^{6} + \frac{83}{71}e^{5} - \frac{159}{71}e^{4} - \frac{1301}{71}e^{3} - \frac{940}{71}e^{2} + \frac{2296}{71}e + \frac{1454}{71}$ |
| 61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $\phantom{-}\frac{27}{142}e^{6} + \frac{109}{142}e^{5} - \frac{163}{71}e^{4} - \frac{847}{71}e^{3} - \frac{376}{71}e^{2} + \frac{1458}{71}e + \frac{1036}{71}$ |
| 79 | $[79, 79, w^{2} - w - 5]$ | $\phantom{-}\frac{8}{71}e^{6} + \frac{6}{71}e^{5} - \frac{186}{71}e^{4} - \frac{118}{71}e^{3} + \frac{1092}{71}e^{2} + \frac{580}{71}e - \frac{622}{71}$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{43}{71}e^{6} + \frac{455}{142}e^{5} - \frac{414}{71}e^{4} - \frac{3421}{71}e^{3} - \frac{2544}{71}e^{2} + \frac{4573}{71}e + \frac{2816}{71}$ |
| 79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $-\frac{22}{71}e^{6} - \frac{175}{142}e^{5} + \frac{263}{71}e^{4} + \frac{1283}{71}e^{3} + \frac{618}{71}e^{2} - \frac{1453}{71}e - \frac{1378}{71}$ |
| 97 | $[97, 97, w^{3} - 6w]$ | $-\frac{24}{71}e^{6} - \frac{249}{142}e^{5} + \frac{203}{71}e^{4} + \frac{1845}{71}e^{3} + \frac{1836}{71}e^{2} - \frac{2166}{71}e - \frac{1968}{71}$ |
| 101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-\frac{61}{142}e^{6} - \frac{156}{71}e^{5} + \frac{292}{71}e^{4} + \frac{2429}{71}e^{3} + \frac{1854}{71}e^{2} - \frac{4217}{71}e - \frac{2714}{71}$ |
| 101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $\phantom{-}\frac{3}{142}e^{6} + \frac{10}{71}e^{5} - \frac{26}{71}e^{4} - \frac{102}{71}e^{3} + \frac{116}{71}e^{2} - \frac{477}{71}e - \frac{516}{71}$ |
| 107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $\phantom{-}\frac{49}{71}e^{6} + \frac{232}{71}e^{5} - \frac{518}{71}e^{4} - \frac{3474}{71}e^{3} - \frac{2222}{71}e^{2} + \frac{4724}{71}e + \frac{2740}{71}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,w^{4}-2w^{3}-4w^{2}+6w+1]$ | $1$ |
| $5$ | $[5,5,w^{4}-w^{3}-5w^{2}+3w+1]$ | $1$ |