Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 22x^{8} + 172x^{6} - 596x^{4} + 875x^{2} - 363\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $-\frac{9}{29}e^{8} + \frac{159}{29}e^{6} - \frac{859}{29}e^{4} + \frac{1632}{29}e^{2} - \frac{745}{29}$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $-\frac{1}{319}e^{9} + \frac{6}{29}e^{7} - \frac{843}{319}e^{5} + \frac{3236}{319}e^{3} - \frac{3218}{319}e$ |
| 7 | $[7, 7, -w^{2} + 11]$ | $\phantom{-}\frac{9}{29}e^{8} - \frac{159}{29}e^{6} + \frac{859}{29}e^{4} - \frac{1661}{29}e^{2} + \frac{803}{29}$ |
| 7 | $[7, 7, -w^{2} + 9]$ | $-\frac{27}{319}e^{9} + \frac{46}{29}e^{7} - \frac{2983}{319}e^{5} + \frac{6346}{319}e^{3} - \frac{3946}{319}e$ |
| 8 | $[8, 2, 2]$ | $-1$ |
| 13 | $[13, 13, -w]$ | $\phantom{-}\frac{67}{319}e^{9} - \frac{112}{29}e^{7} + \frac{7036}{319}e^{5} - \frac{13928}{319}e^{3} + \frac{5704}{319}e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{39}{319}e^{9} + \frac{60}{29}e^{7} - \frac{3210}{319}e^{5} + \frac{4346}{319}e^{3} + \frac{1460}{319}e$ |
| 23 | $[23, 23, w^{2} + w - 10]$ | $-\frac{12}{29}e^{8} + \frac{212}{29}e^{6} - \frac{1155}{29}e^{4} + \frac{2263}{29}e^{2} - \frac{1032}{29}$ |
| 29 | $[29, 29, 2w^{2} - 21]$ | $\phantom{-}\frac{15}{319}e^{9} - \frac{32}{29}e^{7} + \frac{2756}{319}e^{5} - \frac{8027}{319}e^{3} + \frac{6481}{319}e$ |
| 37 | $[37, 37, 2w^{2} + w - 17]$ | $-\frac{39}{319}e^{9} + \frac{60}{29}e^{7} - \frac{3210}{319}e^{5} + \frac{4346}{319}e^{3} + \frac{1460}{319}e$ |
| 43 | $[43, 43, 3w^{2} + 3w - 22]$ | $-\frac{53}{319}e^{9} + \frac{86}{29}e^{7} - \frac{5123}{319}e^{5} + \frac{9137}{319}e^{3} - \frac{1165}{319}e$ |
| 47 | $[47, 47, w^{2} - 6]$ | $-\frac{1}{319}e^{9} + \frac{6}{29}e^{7} - \frac{843}{319}e^{5} + \frac{3555}{319}e^{3} - \frac{5132}{319}e$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{147}{319}e^{9} + \frac{244}{29}e^{7} - \frac{15142}{319}e^{5} + \frac{29092}{319}e^{3} - \frac{9858}{319}e$ |
| 47 | $[47, 47, -w^{2} + 12]$ | $\phantom{-}\frac{32}{29}e^{8} - \frac{575}{29}e^{6} + \frac{3196}{29}e^{4} - \frac{6344}{29}e^{2} + \frac{2955}{29}$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-\frac{260}{319}e^{9} + \frac{429}{29}e^{7} - \frac{26823}{319}e^{5} + \frac{55982}{319}e^{3} - \frac{31524}{319}e$ |
| 61 | $[61, 61, w^{2} - 5]$ | $\phantom{-}\frac{266}{319}e^{9} - \frac{436}{29}e^{7} + \frac{26777}{319}e^{5} - \frac{53387}{319}e^{3} + \frac{25950}{319}e$ |
| 67 | $[67, 67, w^{2} - w - 7]$ | $-\frac{104}{319}e^{9} + \frac{160}{29}e^{7} - \frac{8560}{319}e^{5} + \frac{12121}{319}e^{3} + \frac{597}{319}e$ |
| 73 | $[73, 73, 7w^{2} + 3w - 66]$ | $-\frac{10}{29}e^{8} + \frac{196}{29}e^{6} - \frac{1238}{29}e^{4} + \frac{2838}{29}e^{2} - \frac{1730}{29}$ |
| 79 | $[79, 79, 2w^{2} - 19]$ | $\phantom{-}\frac{34}{29}e^{9} - \frac{620}{29}e^{7} + \frac{3519}{29}e^{5} - \frac{7074}{29}e^{3} + \frac{3185}{29}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, 2]$ | $1$ |