Base field 3.3.1369.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23,23,-w^{2} + 3w + 8]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $41$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + x^{5} - 28x^{4} - 16x^{3} + 213x^{2} + 30x - 229\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{82}{1745}e^{5} - \frac{87}{1745}e^{4} - \frac{1457}{1745}e^{3} + \frac{1627}{1745}e^{2} + \frac{2217}{1745}e - \frac{2854}{1745}$ |
| 11 | $[11, 11, -w^{2} + 3w + 7]$ | $\phantom{-}\frac{19}{1745}e^{5} - \frac{84}{1745}e^{4} - \frac{444}{1745}e^{3} + \frac{909}{1745}e^{2} + \frac{1599}{1745}e + \frac{8617}{1745}$ |
| 11 | $[11, 11, w^{2} - 2w - 8]$ | $\phantom{-}\frac{23}{1745}e^{5} + \frac{82}{1745}e^{4} - \frac{813}{1745}e^{3} - \frac{1012}{1745}e^{2} + \frac{7538}{1745}e + \frac{2349}{1745}$ |
| 23 | $[23, 23, w^{2} - 2w - 7]$ | $-\frac{63}{1745}e^{5} + \frac{3}{1745}e^{4} + \frac{1013}{1745}e^{3} - \frac{718}{1745}e^{2} - \frac{2363}{1745}e + \frac{11471}{1745}$ |
| 23 | $[23, 23, w^{2} - 3w - 8]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w - 1]$ | $-\frac{202}{1745}e^{5} + \frac{342}{1745}e^{4} + \frac{3802}{1745}e^{3} - \frac{6817}{1745}e^{2} - \frac{12867}{1745}e + \frac{14649}{1745}$ |
| 27 | $[27, 3, 3]$ | $-\frac{6}{349}e^{5} + \frac{100}{349}e^{4} + \frac{30}{349}e^{3} - \frac{1481}{349}e^{2} + \frac{1387}{349}e + \frac{1375}{349}$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $-\frac{2}{349}e^{5} - \frac{83}{349}e^{4} + \frac{10}{349}e^{3} + \frac{1135}{349}e^{2} - \frac{352}{349}e + \frac{1389}{349}$ |
| 29 | $[29, 29, w^{2} - 3w - 10]$ | $-\frac{4}{1745}e^{5} - \frac{166}{1745}e^{4} + \frac{369}{1745}e^{3} + \frac{1921}{1745}e^{2} - \frac{5939}{1745}e + \frac{1033}{1745}$ |
| 29 | $[29, 29, w - 3]$ | $\phantom{-}\frac{69}{1745}e^{5} + \frac{246}{1745}e^{4} - \frac{694}{1745}e^{3} - \frac{3036}{1745}e^{2} - \frac{1816}{1745}e + \frac{67}{1745}$ |
| 31 | $[31, 31, w^{2} - 2w - 6]$ | $\phantom{-}\frac{119}{1745}e^{5} + \frac{576}{1745}e^{4} - \frac{2689}{1745}e^{3} - \frac{8726}{1745}e^{2} + \frac{13964}{1745}e + \frac{14202}{1745}$ |
| 31 | $[31, 31, -w^{2} + 3w + 9]$ | $-\frac{149}{1745}e^{5} - \frac{76}{1745}e^{4} + \frac{2839}{1745}e^{3} + \frac{1321}{1745}e^{2} - \frac{8774}{1745}e - \frac{5582}{1745}$ |
| 31 | $[31, 31, w - 2]$ | $-\frac{57}{1745}e^{5} + \frac{252}{1745}e^{4} + \frac{1332}{1745}e^{3} - \frac{4472}{1745}e^{2} - \frac{4797}{1745}e + \frac{3814}{1745}$ |
| 37 | $[37, 37, -w^{2} + 4w + 7]$ | $-\frac{102}{1745}e^{5} - \frac{743}{1745}e^{4} + \frac{1557}{1745}e^{3} + \frac{9723}{1745}e^{2} - \frac{5737}{1745}e - \frac{706}{1745}$ |
| 43 | $[43, 43, 2w^{2} - 6w - 13]$ | $\phantom{-}\frac{147}{1745}e^{5} - \frac{7}{1745}e^{4} - \frac{3527}{1745}e^{3} + \frac{512}{1745}e^{2} + \frac{18892}{1745}e + \frac{3481}{1745}$ |
| 43 | $[43, 43, 2w^{2} - 4w - 17]$ | $-\frac{54}{1745}e^{5} - \frac{496}{1745}e^{4} + \frac{619}{1745}e^{3} + \frac{7611}{1745}e^{2} - \frac{779}{1745}e - \frac{14847}{1745}$ |
| 43 | $[43, 43, w^{2} - 2w - 12]$ | $-\frac{16}{349}e^{5} + \frac{34}{349}e^{4} + \frac{429}{349}e^{3} - \frac{343}{349}e^{2} - \frac{2467}{349}e - \frac{405}{349}$ |
| 47 | $[47, 47, w^{2} - 4w - 4]$ | $\phantom{-}\frac{82}{1745}e^{5} - \frac{87}{1745}e^{4} - \frac{1457}{1745}e^{3} + \frac{1627}{1745}e^{2} + \frac{5707}{1745}e - \frac{9834}{1745}$ |
| 47 | $[47, 47, w^{2} - w - 5]$ | $-\frac{86}{1745}e^{5} - \frac{79}{1745}e^{4} + \frac{1826}{1745}e^{3} + \frac{2039}{1745}e^{2} - \frac{8156}{1745}e - \frac{8328}{1745}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,-w^{2} + 3w + 8]$ | $-1$ |