Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[31, 31, w^{2} - w - 8]$ |
| Dimension: | $34$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $59$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{34} - 3x^{33} - 99x^{32} + 288x^{31} + 4352x^{30} - 12208x^{29} - 112196x^{28} + 301144x^{27} + 1888287x^{26} - 4799296x^{25} - 21870273x^{24} + 51918062x^{23} + 179152085x^{22} - 390348164x^{21} - 1050924076x^{20} + 2057329931x^{19} + 4421532764x^{18} - 7587046658x^{17} - 13234437656x^{16} + 19372839298x^{15} + 27680322236x^{14} - 33602613852x^{13} - 39267092009x^{12} + 38485228048x^{11} + 36015330267x^{10} - 28021815179x^{9} - 19672557463x^{8} + 12363939729x^{7} + 5477138755x^{6} - 3078943196x^{5} - 537950144x^{4} + 338686968x^{3} - 11647376x^{2} - 5592256x + 236864\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 7 | $[7, 7, -w + 2]$ | $...$ |
| 7 | $[7, 7, -w + 1]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $...$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $...$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $...$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}1$ |
| 37 | $[37, 37, -w - 4]$ | $...$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $...$ |
| 47 | $[47, 47, w^{2} - 3]$ | $...$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $...$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $...$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $...$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $...$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, w^{2} - w - 8]$ | $-1$ |