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: | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 6x^{7} - 4x^{6} - 64x^{5} - 21x^{4} + 202x^{3} + 38x^{2} - 217x + 50\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $-\frac{67}{1251}e^{7} - \frac{301}{1251}e^{6} + \frac{47}{139}e^{5} + \frac{2362}{1251}e^{4} + \frac{199}{1251}e^{3} - \frac{877}{417}e^{2} - \frac{1586}{1251}e - \frac{2470}{1251}$ |
| 19 | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $\phantom{-}\frac{479}{1251}e^{7} + \frac{2432}{1251}e^{6} - \frac{280}{139}e^{5} - \frac{21125}{1251}e^{4} - \frac{3794}{1251}e^{3} + \frac{12500}{417}e^{2} + \frac{7399}{1251}e - \frac{9826}{1251}$ |
| 23 | $[23, 23, -w^{2} + w + 2]$ | $-\frac{52}{1251}e^{7} - \frac{439}{1251}e^{6} - \frac{88}{139}e^{5} + \frac{2356}{1251}e^{4} + \frac{8482}{1251}e^{3} + \frac{533}{417}e^{2} - \frac{11519}{1251}e - \frac{3112}{1251}$ |
| 25 | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $\phantom{-}1$ |
| 41 | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $\phantom{-}\frac{310}{1251}e^{7} + \frac{1318}{1251}e^{6} - \frac{288}{139}e^{5} - \frac{10966}{1251}e^{4} + \frac{6884}{1251}e^{3} + \frac{6205}{417}e^{2} - \frac{13462}{1251}e - \frac{7430}{1251}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{112}{1251}e^{7} + \frac{1138}{1251}e^{6} + \frac{243}{139}e^{5} - \frac{8635}{1251}e^{4} - \frac{25390}{1251}e^{3} + \frac{3856}{417}e^{2} + \frac{44345}{1251}e - \frac{11966}{1251}$ |
| 53 | $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ | $\phantom{-}\frac{338}{1251}e^{7} + \frac{977}{1251}e^{6} - \frac{540}{139}e^{5} - \frac{7808}{1251}e^{4} + \frac{26182}{1251}e^{3} + \frac{2582}{417}e^{2} - \frac{49601}{1251}e + \frac{15224}{1251}$ |
| 59 | $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ | $\phantom{-}\frac{43}{139}e^{7} + \frac{77}{139}e^{6} - \frac{842}{139}e^{5} - \frac{740}{139}e^{4} + \frac{4924}{139}e^{3} + \frac{1006}{139}e^{2} - \frac{7708}{139}e + \frac{2274}{139}$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}\frac{499}{1251}e^{7} + \frac{1831}{1251}e^{6} - \frac{599}{139}e^{5} - \frac{15295}{1251}e^{4} + \frac{18926}{1251}e^{3} + \frac{7291}{417}e^{2} - \frac{22525}{1251}e + \frac{3496}{1251}$ |
| 64 | $[64, 2, -2]$ | $-\frac{31}{139}e^{7} - \frac{104}{139}e^{6} + \frac{426}{139}e^{5} + \frac{1041}{139}e^{4} - \frac{1995}{139}e^{3} - \frac{2070}{139}e^{2} + \frac{3459}{139}e - \frac{925}{139}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + w - 3]$ | $\phantom{-}\frac{7}{1251}e^{7} - \frac{398}{1251}e^{6} - \frac{202}{139}e^{5} + \frac{3917}{1251}e^{4} + \frac{15458}{1251}e^{3} - \frac{4763}{417}e^{2} - \frac{28738}{1251}e + \frac{17548}{1251}$ |
| 67 | $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ | $-\frac{179}{417}e^{7} - \frac{1022}{417}e^{6} + \frac{107}{139}e^{5} + \frac{8078}{417}e^{4} + \frac{5990}{417}e^{3} - \frac{3482}{139}e^{2} - \frac{8818}{417}e - \frac{512}{417}$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ | $-\frac{257}{1251}e^{7} - \frac{1472}{1251}e^{6} + \frac{89}{139}e^{5} + \frac{13280}{1251}e^{4} + \frac{7037}{1251}e^{3} - \frac{8312}{417}e^{2} - \frac{11293}{1251}e - \frac{2678}{1251}$ |
| 73 | $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ | $-\frac{473}{1251}e^{7} - \frac{2237}{1251}e^{6} + \frac{365}{139}e^{5} + \frac{19121}{1251}e^{4} - \frac{5653}{1251}e^{3} - \frac{10685}{417}e^{2} + \frac{12647}{1251}e - \frac{4442}{1251}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ | $-\frac{8}{139}e^{7} + \frac{18}{139}e^{6} + \frac{370}{139}e^{5} + \frac{170}{139}e^{4} - \frac{2694}{139}e^{3} - \frac{1839}{139}e^{2} + \frac{4130}{139}e + \frac{676}{139}$ |
| 83 | $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ | $\phantom{-}\frac{130}{417}e^{7} + \frac{889}{417}e^{6} + \frac{104}{139}e^{5} - \frac{7558}{417}e^{4} - \frac{9112}{417}e^{3} + \frac{4853}{139}e^{2} + \frac{13577}{417}e - \frac{9734}{417}$ |
| 89 | $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ | $-\frac{392}{1251}e^{7} - \frac{1481}{1251}e^{6} + \frac{470}{139}e^{5} + \frac{13334}{1251}e^{4} - \frac{14968}{1251}e^{3} - \frac{8909}{417}e^{2} + \frac{18056}{1251}e + \frac{5602}{1251}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{46}{417}e^{7} - \frac{244}{417}e^{6} + \frac{130}{139}e^{5} + \frac{2854}{417}e^{4} - \frac{965}{417}e^{3} - \frac{3212}{139}e^{2} + \frac{2272}{417}e + \frac{6806}{417}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $-\frac{62}{417}e^{7} + \frac{70}{417}e^{6} + \frac{701}{139}e^{5} - \frac{142}{417}e^{4} - \frac{15388}{417}e^{3} - \frac{407}{139}e^{2} + \frac{27629}{417}e - \frac{5186}{417}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $-1$ |