Base field 6.6.1416125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 9x^{3} + 6x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 3x^{8} - 23x^{7} + 67x^{6} + 146x^{5} - 396x^{4} - 172x^{3} + 284x^{2} + 48x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{15}{248}e^{8} + \frac{3}{124}e^{7} + \frac{311}{248}e^{6} - \frac{61}{124}e^{5} - \frac{177}{31}e^{4} + \frac{87}{31}e^{3} - \frac{15}{2}e^{2} - \frac{83}{31}e + \frac{122}{31}$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $-\frac{7}{62}e^{8} + \frac{49}{124}e^{7} + \frac{313}{124}e^{6} - \frac{1079}{124}e^{5} - \frac{1861}{124}e^{4} + \frac{1545}{31}e^{3} + 12e^{2} - \frac{839}{31}e - \frac{12}{31}$ |
| 19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ | $\phantom{-}\frac{1}{62}e^{8} - \frac{7}{124}e^{7} - \frac{29}{62}e^{6} + \frac{163}{124}e^{5} + \frac{134}{31}e^{4} - \frac{265}{31}e^{3} - 13e^{2} + \frac{328}{31}e + \frac{108}{31}$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ | $-\frac{3}{62}e^{8} - \frac{5}{62}e^{7} + \frac{143}{124}e^{6} + \frac{56}{31}e^{5} - \frac{957}{124}e^{4} - \frac{673}{62}e^{3} + 11e^{2} + \frac{318}{31}e - \frac{76}{31}$ |
| 25 | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $-1$ |
| 29 | $[29, 29, -w^{3} + 4w + 1]$ | $\phantom{-}e^{2} - 6$ |
| 41 | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $\phantom{-}\frac{2}{31}e^{8} + \frac{3}{124}e^{7} - \frac{85}{62}e^{6} - \frac{61}{124}e^{5} + \frac{195}{31}e^{4} + \frac{87}{31}e^{3} + 10e^{2} - \frac{145}{31}e - \frac{188}{31}$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ | $-\frac{7}{248}e^{8} - \frac{21}{62}e^{7} + \frac{141}{248}e^{6} + \frac{489}{62}e^{5} - \frac{287}{124}e^{4} - \frac{3025}{62}e^{3} - \frac{9}{2}e^{2} + \frac{1224}{31}e + \frac{28}{31}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ | $\phantom{-}\frac{25}{124}e^{8} + \frac{21}{124}e^{7} - \frac{285}{62}e^{6} - \frac{489}{124}e^{5} + \frac{3445}{124}e^{4} + \frac{702}{31}e^{3} - 22e^{2} - \frac{54}{31}e + \frac{48}{31}$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 2w - 3]$ | $-\frac{5}{62}e^{8} - \frac{29}{62}e^{7} + \frac{57}{31}e^{6} + \frac{331}{31}e^{5} - \frac{329}{31}e^{4} - \frac{1961}{31}e^{3} + 3e^{2} + \frac{1119}{31}e + \frac{266}{31}$ |
| 61 | $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ | $\phantom{-}\frac{19}{248}e^{8} - \frac{41}{124}e^{7} - \frac{427}{248}e^{6} + \frac{937}{124}e^{5} + \frac{653}{62}e^{4} - \frac{1406}{31}e^{3} - \frac{21}{2}e^{2} + \frac{876}{31}e + \frac{48}{31}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{49}{248}e^{8} + \frac{15}{124}e^{7} - \frac{1173}{248}e^{6} - \frac{367}{124}e^{5} + \frac{1006}{31}e^{4} + \frac{590}{31}e^{3} - \frac{105}{2}e^{2} - \frac{508}{31}e + \frac{455}{31}$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $\phantom{-}\frac{1}{62}e^{8} + \frac{6}{31}e^{7} - \frac{27}{124}e^{6} - \frac{275}{62}e^{5} - \frac{177}{124}e^{4} + \frac{820}{31}e^{3} + 20e^{2} - \frac{509}{31}e - \frac{78}{31}$ |
| 71 | $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ | $\phantom{-}\frac{81}{248}e^{8} - \frac{18}{31}e^{7} - \frac{1853}{248}e^{6} + \frac{397}{31}e^{5} + \frac{1427}{31}e^{4} - \frac{2305}{31}e^{3} - \frac{85}{2}e^{2} + \frac{1465}{31}e + \frac{234}{31}$ |
| 79 | $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ | $-\frac{3}{248}e^{8} - \frac{9}{62}e^{7} + \frac{25}{248}e^{6} + \frac{107}{31}e^{5} + \frac{249}{124}e^{4} - \frac{708}{31}e^{3} - \frac{37}{2}e^{2} + \frac{870}{31}e + \frac{322}{31}$ |
| 79 | $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ | $-\frac{21}{248}e^{8} - \frac{1}{62}e^{7} + \frac{547}{248}e^{6} + \frac{41}{62}e^{5} - \frac{2163}{124}e^{4} - \frac{395}{62}e^{3} + \frac{79}{2}e^{2} + \frac{386}{31}e - \frac{350}{31}$ |
| 89 | $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ | $-\frac{13}{124}e^{8} + \frac{15}{62}e^{7} + \frac{71}{31}e^{6} - \frac{168}{31}e^{5} - \frac{1469}{124}e^{4} + \frac{994}{31}e^{3} - 6e^{2} - \frac{675}{31}e + \frac{290}{31}$ |
| 109 | $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ | $\phantom{-}\frac{1}{62}e^{8} + \frac{6}{31}e^{7} - \frac{27}{124}e^{6} - \frac{275}{62}e^{5} - \frac{115}{124}e^{4} + \frac{1609}{62}e^{3} + 14e^{2} - \frac{416}{31}e + \frac{170}{31}$ |
| 109 | $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ | $-\frac{55}{248}e^{8} + \frac{11}{124}e^{7} + \frac{1223}{248}e^{6} - \frac{265}{124}e^{5} - \frac{866}{31}e^{4} + \frac{474}{31}e^{3} + \frac{19}{2}e^{2} - \frac{852}{31}e + \frac{158}{31}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $1$ |