Base field 6.6.300125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[169, 13, -8w^{5} + 2w^{4} + 57w^{3} + 28w^{2} - 34w - 13]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 8x^{3} - 58x^{2} - 488x - 239\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 29 | $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ | $\phantom{-}\frac{37}{754}e^{3} + \frac{50}{377}e^{2} - \frac{1667}{754}e - \frac{1882}{377}$ |
| 29 | $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ | $-\frac{1}{29}e^{3} + \frac{2}{29}e^{2} + \frac{38}{29}e - \frac{182}{29}$ |
| 29 | $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ | $\phantom{-}e$ |
| 29 | $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ | $\phantom{-}\frac{2}{377}e^{3} + \frac{21}{754}e^{2} - \frac{192}{377}e - \frac{3535}{754}$ |
| 29 | $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ | $-\frac{63}{754}e^{3} - \frac{24}{377}e^{2} + \frac{3409}{754}e + \frac{1024}{377}$ |
| 29 | $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ | $-\frac{2}{377}e^{3} - \frac{21}{754}e^{2} + \frac{192}{377}e - \frac{989}{754}$ |
| 41 | $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ | $-\frac{38}{377}e^{3} - \frac{11}{377}e^{2} + \frac{2140}{377}e - \frac{536}{377}$ |
| 41 | $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ | $-\frac{42}{377}e^{3} - \frac{32}{377}e^{2} + \frac{2524}{377}e + \frac{737}{377}$ |
| 41 | $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ | $\phantom{-}\frac{42}{377}e^{3} + \frac{32}{377}e^{2} - \frac{2901}{377}e - \frac{4130}{377}$ |
| 41 | $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ | $\phantom{-}\frac{16}{377}e^{3} + \frac{84}{377}e^{2} - \frac{782}{377}e - \frac{4715}{377}$ |
| 41 | $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ | $\phantom{-}\frac{12}{377}e^{3} + \frac{63}{377}e^{2} - \frac{398}{377}e - \frac{3442}{377}$ |
| 41 | $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ | $-\frac{3}{377}e^{3} - \frac{110}{377}e^{2} + \frac{288}{377}e + \frac{3688}{377}$ |
| 49 | $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ | $\phantom{-}\frac{1}{58}e^{3} - \frac{1}{29}e^{2} - \frac{67}{58}e - \frac{83}{29}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{3}{58}e^{3} - \frac{3}{29}e^{2} - \frac{201}{58}e - \frac{75}{29}$ |
| 71 | $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ | $\phantom{-}\frac{11}{377}e^{3} - \frac{73}{754}e^{2} - \frac{1056}{377}e - \frac{781}{754}$ |
| 71 | $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ | $\phantom{-}\frac{3}{26}e^{3} + \frac{3}{13}e^{2} - \frac{197}{26}e - \frac{154}{13}$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ | $-\frac{7}{377}e^{3} - \frac{131}{377}e^{2} + \frac{295}{377}e + \frac{4961}{377}$ |
| 71 | $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ | $\phantom{-}\frac{59}{377}e^{3} + \frac{27}{377}e^{2} - \frac{3779}{377}e - \frac{3037}{377}$ |
| 71 | $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ | $\phantom{-}\frac{28}{377}e^{3} - \frac{83}{754}e^{2} - \frac{1557}{377}e + \frac{1405}{754}$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ | $-\frac{61}{754}e^{3} - \frac{113}{377}e^{2} + \frac{3971}{754}e + \frac{6078}{377}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $169$ | $[169, 13, -8w^{5} + 2w^{4} + 57w^{3} + 28w^{2} - 34w - 13]$ | $-1$ |