Base field 4.4.11525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{12}{5}w + 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 4x^{6} - 29x^{5} + 81x^{4} + 207x^{3} - 429x^{2} - 197x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ | $\phantom{-}1$ |
| 5 | $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{314}{9127}e^{6} + \frac{2016}{9127}e^{5} + \frac{7482}{9127}e^{4} - \frac{48194}{9127}e^{3} - \frac{53049}{9127}e^{2} + \frac{255780}{9127}e + \frac{74861}{9127}$ |
| 19 | $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ | $-\frac{157}{9127}e^{6} + \frac{1008}{9127}e^{5} + \frac{3741}{9127}e^{4} - \frac{24097}{9127}e^{3} - \frac{31088}{9127}e^{2} + \frac{137017}{9127}e + \frac{60248}{9127}$ |
| 19 | $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ | $\phantom{-}\frac{59}{9127}e^{6} - \frac{30}{9127}e^{5} - \frac{3208}{9127}e^{4} + \frac{5335}{9127}e^{3} + \frac{27437}{9127}e^{2} - \frac{69977}{9127}e + \frac{380}{9127}$ |
| 19 | $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ | $-\frac{157}{9127}e^{6} + \frac{1008}{9127}e^{5} + \frac{3741}{9127}e^{4} - \frac{24097}{9127}e^{3} - \frac{31088}{9127}e^{2} + \frac{137017}{9127}e + \frac{60248}{9127}$ |
| 19 | $[19, 19, w - 1]$ | $\phantom{-}\frac{59}{9127}e^{6} - \frac{30}{9127}e^{5} - \frac{3208}{9127}e^{4} + \frac{5335}{9127}e^{3} + \frac{27437}{9127}e^{2} - \frac{69977}{9127}e + \frac{380}{9127}$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}\frac{655}{9127}e^{6} - \frac{1880}{9127}e^{5} - \frac{21537}{9127}e^{4} + \frac{36178}{9127}e^{3} + \frac{155626}{9127}e^{2} - \frac{211144}{9127}e - \frac{79626}{9127}$ |
| 29 | $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ | $\phantom{-}\frac{655}{9127}e^{6} - \frac{1880}{9127}e^{5} - \frac{21537}{9127}e^{4} + \frac{36178}{9127}e^{3} + \frac{155626}{9127}e^{2} - \frac{211144}{9127}e - \frac{79626}{9127}$ |
| 31 | $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ | $\phantom{-}\frac{445}{9127}e^{6} - \frac{2392}{9127}e^{5} - \frac{9964}{9127}e^{4} + \frac{48128}{9127}e^{3} + \frac{51317}{9127}e^{2} - \frac{239596}{9127}e + \frac{5960}{9127}$ |
| 31 | $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ | $\phantom{-}\frac{445}{9127}e^{6} - \frac{2392}{9127}e^{5} - \frac{9964}{9127}e^{4} + \frac{48128}{9127}e^{3} + \frac{51317}{9127}e^{2} - \frac{239596}{9127}e + \frac{5960}{9127}$ |
| 61 | $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ | $\phantom{-}\frac{625}{9127}e^{6} - \frac{3257}{9127}e^{5} - \frac{17276}{9127}e^{4} + \frac{75697}{9127}e^{3} + \frac{138117}{9127}e^{2} - \frac{430345}{9127}e - \frac{153454}{9127}$ |
| 61 | $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ | $\phantom{-}\frac{625}{9127}e^{6} - \frac{3257}{9127}e^{5} - \frac{17276}{9127}e^{4} + \frac{75697}{9127}e^{3} + \frac{138117}{9127}e^{2} - \frac{430345}{9127}e - \frac{153454}{9127}$ |
| 61 | $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ | $\phantom{-}\frac{1640}{9127}e^{6} - \frac{6867}{9127}e^{5} - \frac{44310}{9127}e^{4} + \frac{130505}{9127}e^{3} + \frac{284803}{9127}e^{2} - \frac{630526}{9127}e - \frac{168574}{9127}$ |
| 61 | $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ | $\phantom{-}\frac{1640}{9127}e^{6} - \frac{6867}{9127}e^{5} - \frac{44310}{9127}e^{4} + \frac{130505}{9127}e^{3} + \frac{284803}{9127}e^{2} - \frac{630526}{9127}e - \frac{168574}{9127}$ |
| 71 | $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ | $-\frac{1539}{9127}e^{6} + \frac{5114}{9127}e^{5} + \frac{46089}{9127}e^{4} - \frac{91052}{9127}e^{3} - \frac{313171}{9127}e^{2} + \frac{473144}{9127}e + \frac{166440}{9127}$ |
| 71 | $[71, 71, w^{2} - 8]$ | $-\frac{1539}{9127}e^{6} + \frac{5114}{9127}e^{5} + \frac{46089}{9127}e^{4} - \frac{91052}{9127}e^{3} - \frac{313171}{9127}e^{2} + \frac{473144}{9127}e + \frac{166440}{9127}$ |
| 79 | $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ | $-\frac{285}{9127}e^{6} + \frac{609}{9127}e^{5} + \frac{8535}{9127}e^{4} - \frac{3340}{9127}e^{3} - \frac{52248}{9127}e^{2} - \frac{24271}{9127}e + \frac{47048}{9127}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ | $-1$ |
| $5$ | $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $-1$ |