Base field 5.5.122821.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + w + 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 2x^{7} - 22x^{6} + 46x^{5} + 120x^{4} - 266x^{3} - 30x^{2} + 94x - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{4} - 2w^{3} - 3w^{2} + 2w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $-\frac{9}{16}e^{7} - \frac{5}{16}e^{6} + \frac{187}{16}e^{5} + \frac{63}{16}e^{4} - \frac{959}{16}e^{3} - \frac{23}{16}e^{2} + \frac{421}{16}e - \frac{11}{16}$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $-\frac{3}{16}e^{7} + \frac{1}{16}e^{6} + \frac{65}{16}e^{5} - \frac{35}{16}e^{4} - \frac{357}{16}e^{3} + \frac{283}{16}e^{2} + \frac{207}{16}e - \frac{97}{16}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ | $-\frac{3}{16}e^{7} + \frac{1}{16}e^{6} + \frac{65}{16}e^{5} - \frac{35}{16}e^{4} - \frac{357}{16}e^{3} + \frac{283}{16}e^{2} + \frac{207}{16}e - \frac{97}{16}$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ | $\phantom{-}\frac{11}{16}e^{7} + \frac{7}{16}e^{6} - \frac{225}{16}e^{5} - \frac{93}{16}e^{4} + \frac{1101}{16}e^{3} + \frac{93}{16}e^{2} - \frac{207}{16}e - \frac{15}{16}$ |
| 23 | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{21}{2}e^{5} + 2e^{4} + \frac{109}{2}e^{3} - 25e^{2} - \frac{45}{2}e + 9$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{3}{8}e^{6} - \frac{19}{8}e^{5} - \frac{57}{8}e^{4} + \frac{87}{8}e^{3} + \frac{249}{8}e^{2} - \frac{61}{8}e - \frac{43}{8}$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 4w - 1]$ | $-\frac{1}{16}e^{7} - \frac{1}{16}e^{6} + \frac{19}{16}e^{5} + \frac{11}{16}e^{4} - \frac{71}{16}e^{3} + \frac{21}{16}e^{2} - \frac{115}{16}e - \frac{55}{16}$ |
| 37 | $[37, 37, w^{4} - 3w^{3} - w^{2} + 5w]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{21}{4}e^{5} + \frac{3}{2}e^{4} + \frac{107}{4}e^{3} - 18e^{2} - \frac{19}{4}e + \frac{11}{2}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 4w^{2} + 3w + 1]$ | $-e^{3} + 11e - 2$ |
| 49 | $[49, 7, -2w^{3} + 4w^{2} + 6w - 5]$ | $\phantom{-}\frac{9}{16}e^{7} + \frac{1}{16}e^{6} - \frac{187}{16}e^{5} + \frac{21}{16}e^{4} + \frac{943}{16}e^{3} - \frac{421}{16}e^{2} - \frac{261}{16}e + \frac{215}{16}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + w^{2} - 7w + 3]$ | $\phantom{-}\frac{9}{16}e^{7} + \frac{1}{16}e^{6} - \frac{187}{16}e^{5} + \frac{21}{16}e^{4} + \frac{943}{16}e^{3} - \frac{421}{16}e^{2} - \frac{229}{16}e + \frac{215}{16}$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - w + 3]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{1}{16}e^{6} - \frac{65}{16}e^{5} + \frac{35}{16}e^{4} + \frac{357}{16}e^{3} - \frac{267}{16}e^{2} - \frac{191}{16}e + \frac{33}{16}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{5}{8}e^{6} - \frac{23}{8}e^{5} + \frac{107}{8}e^{4} + \frac{127}{8}e^{3} - \frac{559}{8}e^{2} + \frac{31}{8}e + \frac{129}{8}$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 4]$ | $-\frac{5}{16}e^{7} + \frac{3}{16}e^{6} + \frac{111}{16}e^{5} - \frac{81}{16}e^{4} - \frac{643}{16}e^{3} + \frac{545}{16}e^{2} + \frac{545}{16}e - \frac{123}{16}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 8w - 2]$ | $-e^{7} - \frac{3}{4}e^{6} + \frac{41}{2}e^{5} + \frac{43}{4}e^{4} - 101e^{3} - \frac{81}{4}e^{2} + \frac{43}{2}e + \frac{41}{4}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 6w - 2]$ | $-\frac{19}{16}e^{7} - \frac{11}{16}e^{6} + \frac{393}{16}e^{5} + \frac{137}{16}e^{4} - \frac{1989}{16}e^{3} - \frac{41}{16}e^{2} + \frac{711}{16}e + \frac{19}{16}$ |
| 103 | $[103, 103, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{1}{8}e^{7} - \frac{3}{8}e^{6} + \frac{19}{8}e^{5} + \frac{57}{8}e^{4} - \frac{87}{8}e^{3} - \frac{241}{8}e^{2} + \frac{45}{8}e - \frac{13}{8}$ |
| 113 | $[113, 113, -2w^{4} + 4w^{3} + 7w^{2} - 7w - 2]$ | $-\frac{1}{4}e^{7} - \frac{1}{4}e^{6} + \frac{21}{4}e^{5} + \frac{17}{4}e^{4} - \frac{111}{4}e^{3} - \frac{55}{4}e^{2} + \frac{63}{4}e + \frac{11}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + w + 2]$ | $-1$ |