Base field 6.6.592661.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 30x^{4} + 54x^{3} + 157x^{2} - 174x - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{5} - 5w^{3} + 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{3} + 3w]$ | $-\frac{109}{4462}e^{5} + \frac{58}{2231}e^{4} + \frac{1546}{2231}e^{3} - \frac{2315}{2231}e^{2} - \frac{14855}{4462}e + \frac{14322}{2231}$ |
| 25 | $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{117}{4462}e^{5} + \frac{226}{2231}e^{4} + \frac{1639}{2231}e^{3} - \frac{6251}{2231}e^{2} - \frac{9109}{4462}e + \frac{16110}{2231}$ |
| 31 | $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ | $\phantom{-}\frac{1}{2231}e^{5} - \frac{42}{2231}e^{4} - \frac{581}{2231}e^{3} + \frac{984}{2231}e^{2} + \frac{9879}{2231}e + \frac{1784}{2231}$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-1$ |
| 37 | $[37, 37, w^{4} - 5w^{2} + w + 3]$ | $\phantom{-}\frac{223}{4462}e^{5} - \frac{221}{2231}e^{4} - \frac{3429}{2231}e^{3} + \frac{4859}{2231}e^{2} + \frac{38947}{4462}e - \frac{10798}{2231}$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ | $-\frac{3}{2231}e^{5} + \frac{126}{2231}e^{4} - \frac{488}{2231}e^{3} - \frac{2952}{2231}e^{2} + \frac{10521}{2231}e + \frac{3572}{2231}$ |
| 47 | $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ | $-\frac{109}{2231}e^{5} + \frac{116}{2231}e^{4} + \frac{3092}{2231}e^{3} - \frac{2399}{2231}e^{2} - \frac{10393}{2231}e + \frac{1872}{2231}$ |
| 49 | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ | $-\frac{103}{4462}e^{5} - \frac{68}{2231}e^{4} + \frac{2034}{2231}e^{3} + \frac{637}{2231}e^{2} - \frac{31435}{4462}e + \frac{10750}{2231}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ | $\phantom{-}\frac{117}{4462}e^{5} - \frac{226}{2231}e^{4} - \frac{1639}{2231}e^{3} + \frac{6251}{2231}e^{2} + \frac{18033}{4462}e - \frac{16110}{2231}$ |
| 59 | $[59, 59, w^{4} - 5w^{2} - w + 5]$ | $\phantom{-}\frac{327}{2231}e^{5} - \frac{348}{2231}e^{4} - \frac{9276}{2231}e^{3} + \frac{9428}{2231}e^{2} + \frac{40103}{2231}e - \frac{14540}{2231}$ |
| 61 | $[61, 61, w^{3} - w^{2} - 3w]$ | $-\frac{547}{4462}e^{5} + \frac{332}{2231}e^{4} + \frac{8311}{2231}e^{3} - \frac{8097}{2231}e^{2} - \frac{89571}{4462}e + \frac{16282}{2231}$ |
| 64 | $[64, 2, -2]$ | $-\frac{53}{2231}e^{5} - \frac{5}{2231}e^{4} + \frac{1790}{2231}e^{3} - \frac{839}{2231}e^{2} - \frac{14919}{2231}e + \frac{14767}{2231}$ |
| 67 | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ | $-\frac{1}{2231}e^{5} + \frac{42}{2231}e^{4} + \frac{581}{2231}e^{3} - \frac{984}{2231}e^{2} - \frac{14341}{2231}e + \frac{7140}{2231}$ |
| 67 | $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ | $-\frac{170}{2231}e^{5} + \frac{447}{2231}e^{4} + \frac{5068}{2231}e^{3} - \frac{11110}{2231}e^{2} - \frac{24028}{2231}e + \frac{26908}{2231}$ |
| 73 | $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ | $-\frac{133}{4462}e^{5} + \frac{562}{2231}e^{4} + \frac{1825}{2231}e^{3} - \frac{14123}{2231}e^{2} - \frac{6541}{4462}e + \frac{37534}{2231}$ |
| 73 | $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ | $-\frac{553}{4462}e^{5} + \frac{458}{2231}e^{4} + \frac{7823}{2231}e^{3} - \frac{11049}{2231}e^{2} - \frac{68529}{4462}e + \frac{19854}{2231}$ |
| 83 | $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ | $\phantom{-}\frac{114}{2231}e^{5} - \frac{326}{2231}e^{4} - \frac{3766}{2231}e^{3} + \frac{9550}{2231}e^{2} + \frac{19630}{2231}e - \frac{37572}{2231}$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ | $\phantom{-}\frac{15}{194}e^{5} - \frac{24}{97}e^{4} - \frac{235}{97}e^{3} + \frac{590}{97}e^{2} + \frac{2879}{194}e - \frac{1558}{97}$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ | $\phantom{-}\frac{109}{4462}e^{5} - \frac{58}{2231}e^{4} - \frac{1546}{2231}e^{3} + \frac{2315}{2231}e^{2} + \frac{14855}{4462}e - \frac{5398}{2231}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $1$ |