Base field 4.4.16225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 6x + 36\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[36, 6, -w]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + 4x^{10} - 16x^{9} - 80x^{8} + 7x^{7} + 334x^{6} + 215x^{5} - 362x^{4} - 283x^{3} + 81x^{2} + 81x + 10\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ | $-1$ |
| 9 | $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ | $...$ |
| 11 | $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ | $-\frac{10372}{78891}e^{10} - \frac{12590}{26297}e^{9} + \frac{168082}{78891}e^{8} + \frac{747907}{78891}e^{7} - \frac{128567}{78891}e^{6} - \frac{2995244}{78891}e^{5} - \frac{612225}{26297}e^{4} + \frac{2883101}{78891}e^{3} + \frac{1865534}{78891}e^{2} - \frac{574004}{78891}e - \frac{230272}{78891}$ |
| 19 | $[19, 19, w + 1]$ | $-\frac{7454}{26297}e^{10} - \frac{30440}{26297}e^{9} + \frac{123320}{26297}e^{8} + \frac{616310}{26297}e^{7} - \frac{133262}{26297}e^{6} - \frac{2694502}{26297}e^{5} - \frac{1237753}{26297}e^{4} + \frac{3348313}{26297}e^{3} + \frac{1624790}{26297}e^{2} - \frac{1175850}{26297}e - \frac{432860}{26297}$ |
| 19 | $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ | $...$ |
| 25 | $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ | $...$ |
| 29 | $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ | $-\frac{9097}{78891}e^{10} - \frac{2204}{26297}e^{9} + \frac{214978}{78891}e^{8} + \frac{153499}{78891}e^{7} - \frac{1451894}{78891}e^{6} - \frac{863120}{78891}e^{5} + \frac{1220666}{26297}e^{4} + \frac{1684232}{78891}e^{3} - \frac{2987068}{78891}e^{2} - \frac{1034231}{78891}e + \frac{248045}{78891}$ |
| 29 | $[29, 29, w - 1]$ | $...$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ | $...$ |
| 31 | $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ | $-\frac{13862}{78891}e^{10} - \frac{13794}{26297}e^{9} + \frac{261848}{78891}e^{8} + \frac{857771}{78891}e^{7} - \frac{885817}{78891}e^{6} - \frac{3993691}{78891}e^{5} + \frac{24437}{26297}e^{4} + \frac{5707762}{78891}e^{3} + \frac{1213717}{78891}e^{2} - \frac{2204131}{78891}e - \frac{371342}{78891}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ | $...$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ | $...$ |
| 59 | $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $-\frac{7037}{26297}e^{10} - \frac{20002}{26297}e^{9} + \frac{138534}{26297}e^{8} + \frac{423203}{26297}e^{7} - \frac{561489}{26297}e^{6} - \frac{2095430}{26297}e^{5} + \frac{503340}{26297}e^{4} + \frac{3389525}{26297}e^{3} + \frac{153658}{26297}e^{2} - \frac{1552278}{26297}e - \frac{207060}{26297}$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ | $...$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ | $...$ |
| 79 | $[79, 79, w^{2} - 11]$ | $...$ |
| 79 | $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ | $...$ |
| 89 | $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ | $-1$ |
| $9$ | $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ | $1$ |