Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[17, 17, -w^{2} + 3w + 1]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} - 18x^{10} + 116x^{8} - 316x^{6} + 332x^{4} - 132x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{8}e^{11} - \frac{9}{4}e^{9} + 14e^{7} - \frac{67}{2}e^{5} + \frac{43}{2}e^{3} - \frac{7}{2}e$ |
5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $-\frac{1}{4}e^{10} + \frac{9}{2}e^{8} - \frac{57}{2}e^{6} + 73e^{4} - 62e^{2} + 12$ |
8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{1}{8}e^{11} + \frac{9}{4}e^{9} - \frac{29}{2}e^{7} + 39e^{5} - \frac{75}{2}e^{3} + \frac{19}{2}e$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{11} + 9e^{9} - 57e^{7} + \frac{291}{2}e^{5} - 120e^{3} + 21e$ |
17 | $[17, 17, -w^{2} + 3w + 1]$ | $\phantom{-}1$ |
23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}\frac{1}{2}e^{11} - 9e^{9} + \frac{115}{2}e^{7} - 151e^{5} + 136e^{3} - 28e$ |
25 | $[25, 5, -w^{2} + 2w + 1]$ | $-\frac{13}{8}e^{11} + \frac{113}{4}e^{9} - 172e^{7} + 419e^{5} - \frac{651}{2}e^{3} + \frac{129}{2}e$ |
37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $\phantom{-}e^{11} - \frac{35}{2}e^{9} + 108e^{7} - 272e^{5} + 235e^{3} - 56e$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{1}{4}e^{11} + 4e^{9} - \frac{41}{2}e^{7} + \frac{59}{2}e^{5} + 26e^{3} - 30e$ |
49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $\phantom{-}\frac{3}{8}e^{11} - \frac{25}{4}e^{9} + \frac{73}{2}e^{7} - 86e^{5} + \frac{131}{2}e^{3} - \frac{7}{2}e$ |
49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}\frac{5}{4}e^{11} - \frac{43}{2}e^{9} + 129e^{7} - \frac{611}{2}e^{5} + 215e^{3} - 27e$ |
59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}\frac{3}{2}e^{10} - 26e^{8} + 157e^{6} - 376e^{4} + 281e^{2} - 51$ |
67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $-\frac{1}{2}e^{8} + 6e^{6} - 21e^{4} + 19e^{2} - 5$ |
71 | $[71, 71, 2w - 3]$ | $-\frac{7}{8}e^{11} + \frac{63}{4}e^{9} - \frac{199}{2}e^{7} + 252e^{5} - \frac{409}{2}e^{3} + \frac{83}{2}e$ |
71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{15}{2}e^{6} + 37e^{4} - 66e^{2} + 20$ |
79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $\phantom{-}\frac{1}{2}e^{11} - 9e^{9} + \frac{113}{2}e^{7} - 141e^{5} + 114e^{3} - 36e$ |
79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $\phantom{-}\frac{3}{2}e^{11} - \frac{53}{2}e^{9} + \frac{329}{2}e^{7} - \frac{821}{2}e^{5} + 331e^{3} - 72e$ |
81 | $[81, 3, -3]$ | $-e^{10} + \frac{33}{2}e^{8} - 95e^{6} + 220e^{4} - 169e^{2} + 25$ |
83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $\phantom{-}\frac{11}{8}e^{11} - \frac{95}{4}e^{9} + 143e^{7} - \frac{679}{2}e^{5} + \frac{479}{2}e^{3} - \frac{63}{2}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{2} + 3w + 1]$ | $-1$ |