Base field 3.3.1593.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w + 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 19x^{8} + 115x^{6} - 248x^{4} + 178x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{22}{97}e^{8} - \frac{377}{97}e^{6} + \frac{1823}{97}e^{4} - \frac{1966}{97}e^{2} - \frac{180}{97}$ |
| 5 | $[5, 5, w^{2} - 2w - 4]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{23}{194}e^{9} - \frac{425}{194}e^{7} + \frac{2457}{194}e^{5} - \frac{2443}{97}e^{3} + \frac{1696}{97}e$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{43}{194}e^{9} - \frac{803}{194}e^{7} + \frac{4661}{194}e^{5} - \frac{4483}{97}e^{3} + \frac{2496}{97}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{19}{97}e^{8} - \frac{330}{97}e^{6} + \frac{1667}{97}e^{4} - \frac{2227}{97}e^{2} + \frac{453}{97}$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $-\frac{48}{97}e^{9} + \frac{849}{97}e^{7} - \frac{4436}{97}e^{5} + \frac{6591}{97}e^{3} - \frac{2191}{97}e$ |
| 17 | $[17, 17, w - 2]$ | $-\frac{15}{194}e^{9} + \frac{235}{194}e^{7} - \frac{877}{194}e^{5} - \frac{216}{97}e^{3} + \frac{1243}{97}e$ |
| 25 | $[25, 5, -w^{2} - w + 3]$ | $\phantom{-}\frac{7}{194}e^{9} - \frac{45}{194}e^{7} - \frac{703}{194}e^{5} + \frac{2875}{97}e^{3} - \frac{4085}{97}e$ |
| 29 | $[29, 29, w^{2} - 2w - 6]$ | $\phantom{-}\frac{3}{97}e^{8} - \frac{47}{97}e^{6} + \frac{156}{97}e^{4} + \frac{164}{97}e^{2} + \frac{46}{97}$ |
| 31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}\frac{26}{97}e^{9} - \frac{472}{97}e^{7} + \frac{2613}{97}e^{5} - \frac{4625}{97}e^{3} + \frac{2468}{97}e$ |
| 37 | $[37, 37, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{67}{194}e^{9} - \frac{1179}{194}e^{7} + \frac{6103}{194}e^{5} - \frac{4506}{97}e^{3} + \frac{2001}{97}e$ |
| 41 | $[41, 41, w^{2} - 8]$ | $\phantom{-}\frac{54}{97}e^{9} - \frac{943}{97}e^{7} + \frac{4748}{97}e^{5} - \frac{5972}{97}e^{3} + \frac{343}{97}e$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{16}{97}e^{9} + \frac{283}{97}e^{7} - \frac{1511}{97}e^{5} + \frac{2488}{97}e^{3} - \frac{1086}{97}e$ |
| 53 | $[53, 53, 2w^{2} - 5w - 4]$ | $-\frac{101}{97}e^{8} + \frac{1744}{97}e^{6} - \frac{8550}{97}e^{4} + \frac{9740}{97}e^{2} + \frac{262}{97}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{43}{97}e^{9} + \frac{706}{97}e^{7} - \frac{3012}{97}e^{5} + \frac{1109}{97}e^{3} + \frac{3350}{97}e$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $\phantom{-}\frac{1}{97}e^{8} - \frac{48}{97}e^{6} + \frac{537}{97}e^{4} - \frac{1756}{97}e^{2} + \frac{1244}{97}$ |
| 61 | $[61, 61, -w^{2} + 2w + 12]$ | $\phantom{-}\frac{34}{97}e^{8} - \frac{565}{97}e^{6} + \frac{2641}{97}e^{4} - \frac{2862}{97}e^{2} + \frac{198}{97}$ |
| 67 | $[67, 67, -2w^{2} + 6w + 3]$ | $-\frac{167}{194}e^{9} + \frac{2875}{194}e^{7} - \frac{14019}{194}e^{5} + \frac{7722}{97}e^{3} + \frac{886}{97}e$ |
| 71 | $[71, 71, w^{2} - w - 11]$ | $-\frac{1}{97}e^{8} + \frac{48}{97}e^{6} - \frac{537}{97}e^{4} + \frac{1950}{97}e^{2} - \frac{1632}{97}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 3]$ | $-1$ |