Base field 6.6.592661.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, w^{4} - 5w^{2} - w + 5]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 4x^{7} - 30x^{6} + 132x^{5} + 197x^{4} - 1144x^{3} + 176x^{2} + 2176x - 1280\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{5} - 5w^{3} + 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{3} + 3w]$ | $\phantom{-}\frac{23}{32}e^{7} - \frac{1}{2}e^{6} - \frac{371}{16}e^{5} + \frac{73}{4}e^{4} + \frac{6439}{32}e^{3} - \frac{315}{2}e^{2} - 390e + 280$ |
| 25 | $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{1}{8}e^{6} - 6e^{5} + \frac{37}{8}e^{4} + \frac{821}{16}e^{3} - \frac{81}{2}e^{2} - \frac{191}{2}e + 76$ |
| 31 | $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ | $-\frac{11}{64}e^{7} + \frac{1}{8}e^{6} + \frac{177}{32}e^{5} - \frac{71}{16}e^{4} - \frac{3039}{64}e^{3} + \frac{591}{16}e^{2} + 88e - 61$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-\frac{55}{32}e^{7} + \frac{19}{16}e^{6} + \frac{887}{16}e^{5} - \frac{347}{8}e^{4} - \frac{15375}{32}e^{3} + \frac{5991}{16}e^{2} + \frac{1851}{2}e - 664$ |
| 37 | $[37, 37, w^{4} - 5w^{2} + w + 3]$ | $\phantom{-}e^{7} - \frac{5}{8}e^{6} - \frac{129}{4}e^{5} + \frac{93}{4}e^{4} + \frac{1119}{4}e^{3} - \frac{1621}{8}e^{2} - \frac{1083}{2}e + 370$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ | $-\frac{37}{32}e^{7} + \frac{3}{4}e^{6} + \frac{597}{16}e^{5} - \frac{111}{4}e^{4} - \frac{10365}{32}e^{3} + \frac{967}{4}e^{2} + 625e - 436$ |
| 47 | $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ | $\phantom{-}\frac{67}{64}e^{7} - \frac{3}{4}e^{6} - \frac{1081}{32}e^{5} + \frac{435}{16}e^{4} + \frac{18743}{64}e^{3} - \frac{3745}{16}e^{2} - 564e + 417$ |
| 49 | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ | $-\frac{5}{32}e^{7} + \frac{1}{8}e^{6} + \frac{81}{16}e^{5} - \frac{9}{2}e^{4} - \frac{1413}{32}e^{3} + \frac{309}{8}e^{2} + 86e - 66$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ | $\phantom{-}\frac{55}{64}e^{7} - \frac{9}{16}e^{6} - \frac{889}{32}e^{5} + \frac{331}{16}e^{4} + \frac{15475}{64}e^{3} - \frac{719}{4}e^{2} - \frac{1879}{4}e + 327$ |
| 59 | $[59, 59, w^{4} - 5w^{2} - w + 5]$ | $-1$ |
| 61 | $[61, 61, w^{3} - w^{2} - 3w]$ | $\phantom{-}\frac{21}{16}e^{7} - \frac{7}{8}e^{6} - \frac{339}{8}e^{5} + \frac{129}{4}e^{4} + \frac{5889}{16}e^{3} - \frac{2247}{8}e^{2} - \frac{1427}{2}e + 510$ |
| 64 | $[64, 2, -2]$ | $-\frac{25}{16}e^{7} + \frac{17}{16}e^{6} + \frac{403}{8}e^{5} - \frac{311}{8}e^{4} - \frac{6977}{16}e^{3} + \frac{5381}{16}e^{2} + \frac{3343}{4}e - 600$ |
| 67 | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ | $\phantom{-}\frac{17}{16}e^{7} - \frac{11}{16}e^{6} - \frac{137}{4}e^{5} + \frac{101}{4}e^{4} + \frac{4747}{16}e^{3} - \frac{3489}{16}e^{2} - 571e + 393$ |
| 67 | $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ | $\phantom{-}\frac{47}{32}e^{7} - e^{6} - \frac{757}{16}e^{5} + \frac{293}{8}e^{4} + \frac{13091}{32}e^{3} - \frac{2535}{8}e^{2} - 783e + 568$ |
| 73 | $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ | $\phantom{-}\frac{19}{64}e^{7} - \frac{3}{16}e^{6} - \frac{305}{32}e^{5} + \frac{113}{16}e^{4} + \frac{5255}{64}e^{3} - 62e^{2} - \frac{625}{4}e + 109$ |
| 73 | $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ | $-\frac{13}{8}e^{7} + \frac{9}{8}e^{6} + \frac{419}{8}e^{5} - \frac{329}{8}e^{4} - \frac{1813}{4}e^{3} + \frac{711}{2}e^{2} + 869e - 632$ |
| 83 | $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ | $\phantom{-}\frac{9}{16}e^{7} - \frac{3}{8}e^{6} - \frac{145}{8}e^{5} + \frac{55}{4}e^{4} + \frac{2513}{16}e^{3} - \frac{955}{8}e^{2} - \frac{609}{2}e + 220$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ | $\phantom{-}\frac{3}{4}e^{7} - \frac{9}{16}e^{6} - \frac{193}{8}e^{5} + \frac{81}{4}e^{4} + \frac{1663}{8}e^{3} - \frac{2779}{16}e^{2} - \frac{791}{2}e + 307$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ | $\phantom{-}\frac{35}{16}e^{7} - \frac{3}{2}e^{6} - \frac{565}{8}e^{5} + 55e^{4} + \frac{9815}{16}e^{3} - \frac{957}{2}e^{2} - 1188e + 866$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, w^{4} - 5w^{2} - w + 5]$ | $1$ |