Base field 4.4.17989.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 25, w - 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 24x^{8} - 4x^{7} + 194x^{6} + 59x^{5} - 638x^{4} - 217x^{3} + 860x^{2} + 225x - 375\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $-\frac{218}{675}e^{9} + \frac{68}{135}e^{8} + \frac{4807}{675}e^{7} - \frac{244}{25}e^{6} - \frac{34327}{675}e^{5} + \frac{39598}{675}e^{4} + \frac{92894}{675}e^{3} - \frac{89264}{675}e^{2} - \frac{5519}{45}e + \frac{872}{9}$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}\frac{58}{675}e^{9} - \frac{19}{135}e^{8} - \frac{1217}{675}e^{7} + \frac{197}{75}e^{6} + \frac{7832}{675}e^{5} - \frac{9833}{675}e^{4} - \frac{16534}{675}e^{3} + \frac{18949}{675}e^{2} + \frac{508}{45}e - \frac{151}{9}$ |
| 16 | $[16, 2, 2]$ | $-\frac{218}{675}e^{9} + \frac{68}{135}e^{8} + \frac{4807}{675}e^{7} - \frac{244}{25}e^{6} - \frac{34327}{675}e^{5} + \frac{39598}{675}e^{4} + \frac{92894}{675}e^{3} - \frac{89264}{675}e^{2} - \frac{5474}{45}e + \frac{881}{9}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{32}{225}e^{9} + \frac{1}{9}e^{8} + \frac{718}{225}e^{7} - \frac{149}{75}e^{6} - \frac{5158}{225}e^{5} + \frac{2587}{225}e^{4} + \frac{13466}{225}e^{3} - \frac{7256}{225}e^{2} - \frac{728}{15}e + \frac{107}{3}$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $-\frac{218}{675}e^{9} + \frac{10}{27}e^{8} + \frac{4807}{675}e^{7} - \frac{517}{75}e^{6} - \frac{33967}{675}e^{5} + \frac{26638}{675}e^{4} + \frac{88484}{675}e^{3} - \frac{59519}{675}e^{2} - \frac{4907}{45}e + \frac{620}{9}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{19}{135}e^{9} + \frac{7}{27}e^{8} + \frac{401}{135}e^{7} - \frac{76}{15}e^{6} - \frac{2651}{135}e^{5} + \frac{4094}{135}e^{4} + \frac{6307}{135}e^{3} - \frac{8722}{135}e^{2} - \frac{325}{9}e + \frac{380}{9}$ |
| 27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $\phantom{-}\frac{11}{675}e^{9} - \frac{14}{135}e^{8} - \frac{289}{675}e^{7} + \frac{179}{75}e^{6} + \frac{2764}{675}e^{5} - \frac{11806}{675}e^{4} - \frac{11048}{675}e^{3} + \frac{30323}{675}e^{2} + \frac{175}{9}e - \frac{296}{9}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $\phantom{-}\frac{218}{675}e^{9} - \frac{10}{27}e^{8} - \frac{4807}{675}e^{7} + \frac{517}{75}e^{6} + \frac{33967}{675}e^{5} - \frac{26638}{675}e^{4} - \frac{88484}{675}e^{3} + \frac{58844}{675}e^{2} + \frac{4907}{45}e - \frac{584}{9}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $\phantom{-}\frac{107}{675}e^{9} - \frac{29}{135}e^{8} - \frac{2443}{675}e^{7} + \frac{328}{75}e^{6} + \frac{18238}{675}e^{5} - \frac{19567}{675}e^{4} - \frac{51446}{675}e^{3} + \frac{51416}{675}e^{2} + \frac{3059}{45}e - \frac{590}{9}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}\frac{133}{675}e^{9} - \frac{31}{135}e^{8} - \frac{2942}{675}e^{7} + \frac{332}{75}e^{6} + \frac{20897}{675}e^{5} - \frac{18398}{675}e^{4} - \frac{54724}{675}e^{3} + \frac{45754}{675}e^{2} + \frac{2986}{45}e - \frac{523}{9}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}\frac{191}{675}e^{9} - \frac{68}{135}e^{8} - \frac{4159}{675}e^{7} + \frac{248}{25}e^{6} + \frac{29089}{675}e^{5} - \frac{41191}{675}e^{4} - \frac{76343}{675}e^{3} + \frac{95123}{675}e^{2} + \frac{4466}{45}e - \frac{917}{9}$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{217}{675}e^{9} - \frac{14}{27}e^{8} - \frac{4658}{675}e^{7} + \frac{748}{75}e^{6} + \frac{31748}{675}e^{5} - \frac{40022}{675}e^{4} - \frac{79621}{675}e^{3} + \frac{89461}{675}e^{2} + \frac{4393}{45}e - \frac{850}{9}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}\frac{64}{225}e^{9} - \frac{16}{45}e^{8} - \frac{1436}{225}e^{7} + \frac{171}{25}e^{6} + \frac{10436}{225}e^{5} - \frac{9269}{225}e^{4} - \frac{28402}{225}e^{3} + \frac{21502}{225}e^{2} + \frac{335}{3}e - \frac{205}{3}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{1}{9}e^{9} + \frac{2}{9}e^{8} + \frac{23}{9}e^{7} - \frac{14}{3}e^{6} - \frac{179}{9}e^{5} + \frac{287}{9}e^{4} + \frac{568}{9}e^{3} - \frac{754}{9}e^{2} - \frac{206}{3}e + \frac{202}{3}$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $-\frac{73}{675}e^{9} + \frac{7}{135}e^{8} + \frac{1427}{675}e^{7} - \frac{22}{75}e^{6} - \frac{7727}{675}e^{5} - \frac{3142}{675}e^{4} + \frac{8764}{675}e^{3} + \frac{17036}{675}e^{2} + \frac{79}{9}e - \frac{239}{9}$ |
| 71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $\phantom{-}\frac{49}{675}e^{9} - \frac{2}{27}e^{8} - \frac{1226}{675}e^{7} + \frac{131}{75}e^{6} + \frac{10406}{675}e^{5} - \frac{9734}{675}e^{4} - \frac{34912}{675}e^{3} + \frac{32467}{675}e^{2} + \frac{2641}{45}e - \frac{430}{9}$ |
| 89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $-\frac{59}{75}e^{9} + \frac{19}{15}e^{8} + \frac{1291}{75}e^{7} - \frac{1844}{75}e^{6} - \frac{9101}{75}e^{5} + \frac{11074}{75}e^{4} + \frac{8049}{25}e^{3} - \frac{24682}{75}e^{2} - \frac{1392}{5}e + 236$ |
| 97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}\frac{218}{675}e^{9} - \frac{68}{135}e^{8} - \frac{4807}{675}e^{7} + \frac{244}{25}e^{6} + \frac{34327}{675}e^{5} - \frac{39598}{675}e^{4} - \frac{92894}{675}e^{3} + \frac{89264}{675}e^{2} + \frac{5654}{45}e - \frac{890}{9}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $1$ |