Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, w^{3} + w^{2} - 4w - 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 6x^{7} - 7x^{6} - 86x^{5} - 78x^{4} + 140x^{3} + 69x^{2} - 88x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $-\frac{5}{24}e^{7} - \frac{4}{3}e^{6} + \frac{7}{8}e^{5} + \frac{109}{6}e^{4} + \frac{293}{12}e^{3} - \frac{37}{2}e^{2} - \frac{197}{8}e + \frac{59}{6}$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{1}{12}e^{7} - \frac{7}{12}e^{6} + \frac{43}{6}e^{4} + \frac{167}{12}e^{3} + \frac{5}{2}e^{2} - \frac{29}{4}e - \frac{11}{3}$ |
| 25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $\phantom{-}\frac{1}{6}e^{7} + \frac{7}{6}e^{6} - \frac{1}{4}e^{5} - \frac{95}{6}e^{4} - \frac{313}{12}e^{3} + \frac{59}{4}e^{2} + \frac{121}{4}e - \frac{29}{3}$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-\frac{7}{24}e^{7} - \frac{23}{12}e^{6} + \frac{11}{8}e^{5} + \frac{82}{3}e^{4} + \frac{191}{6}e^{3} - \frac{83}{2}e^{2} - \frac{267}{8}e + \frac{109}{6}$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $\phantom{-}\frac{25}{24}e^{7} + \frac{83}{12}e^{6} - \frac{27}{8}e^{5} - \frac{280}{3}e^{4} - \frac{1597}{12}e^{3} + \frac{325}{4}e^{2} + \frac{863}{8}e - \frac{253}{6}$ |
| 59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $\phantom{-}\frac{1}{4}e^{7} + 2e^{6} + e^{5} - \frac{101}{4}e^{4} - 56e^{3} - \frac{3}{4}e^{2} + \frac{177}{4}e - 3$ |
| 59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $\phantom{-}\frac{5}{8}e^{7} + 4e^{6} - \frac{21}{8}e^{5} - 54e^{4} - \frac{287}{4}e^{3} + \frac{93}{2}e^{2} + \frac{443}{8}e - \frac{27}{2}$ |
| 61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $\phantom{-}\frac{9}{8}e^{7} + \frac{29}{4}e^{6} - \frac{37}{8}e^{5} - \frac{393}{4}e^{4} - 131e^{3} + \frac{363}{4}e^{2} + \frac{859}{8}e - \frac{83}{2}$ |
| 61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $-\frac{1}{6}e^{7} - \frac{7}{6}e^{6} + \frac{1}{4}e^{5} + \frac{46}{3}e^{4} + \frac{295}{12}e^{3} - \frac{27}{4}e^{2} - \frac{55}{4}e - \frac{13}{3}$ |
| 64 | $[64, 2, 2]$ | $\phantom{-}\frac{1}{12}e^{7} + \frac{5}{6}e^{6} + \frac{5}{4}e^{5} - \frac{113}{12}e^{4} - \frac{359}{12}e^{3} - \frac{29}{2}e^{2} + 14e + \frac{17}{3}$ |
| 71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $-\frac{5}{24}e^{7} - \frac{4}{3}e^{6} + \frac{7}{8}e^{5} + \frac{221}{12}e^{4} + \frac{74}{3}e^{3} - \frac{43}{2}e^{2} - \frac{211}{8}e + \frac{53}{6}$ |
| 71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $-\frac{11}{24}e^{7} - \frac{37}{12}e^{6} + \frac{9}{8}e^{5} + \frac{122}{3}e^{4} + \frac{755}{12}e^{3} - \frac{95}{4}e^{2} - \frac{381}{8}e + \frac{47}{6}$ |
| 79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $\phantom{-}\frac{1}{3}e^{7} + \frac{25}{12}e^{6} - \frac{7}{4}e^{5} - \frac{175}{6}e^{4} - \frac{419}{12}e^{3} + \frac{79}{2}e^{2} + 43e - \frac{64}{3}$ |
| 81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $-\frac{3}{8}e^{7} - \frac{5}{2}e^{6} + \frac{5}{8}e^{5} + \frac{127}{4}e^{4} + \frac{223}{4}e^{3} - \frac{19}{4}e^{2} - \frac{341}{8}e + \frac{5}{2}$ |
| 89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $-\frac{2}{3}e^{7} - \frac{25}{6}e^{6} + \frac{15}{4}e^{5} + \frac{703}{12}e^{4} + \frac{389}{6}e^{3} - \frac{319}{4}e^{2} - 64e + \frac{98}{3}$ |
| 89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $\phantom{-}\frac{5}{12}e^{7} + \frac{29}{12}e^{6} - \frac{11}{4}e^{5} - \frac{97}{3}e^{4} - \frac{100}{3}e^{3} + \frac{105}{4}e^{2} + 11e - \frac{32}{3}$ |
| 89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $\phantom{-}\frac{11}{24}e^{7} + \frac{37}{12}e^{6} - \frac{5}{8}e^{5} - \frac{235}{6}e^{4} - \frac{839}{12}e^{3} + \frac{21}{4}e^{2} + \frac{389}{8}e - \frac{35}{6}$ |
| 89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $-\frac{3}{4}e^{7} - \frac{9}{2}e^{6} + \frac{17}{4}e^{5} + \frac{121}{2}e^{4} + \frac{143}{2}e^{3} - 52e^{2} - \frac{203}{4}e + 17$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $-1$ |