Base field \(\Q(\sqrt{114}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 114\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[3, 3, w]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 19x^{6} + 87x^{4} - 116x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -3w - 32]$ | $\phantom{-}\frac{1}{76}e^{7} - \frac{9}{76}e^{5} - \frac{79}{76}e^{3} + \frac{155}{38}e$ |
3 | $[3, 3, w]$ | $\phantom{-}1$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 3]$ | $-\frac{1}{76}e^{7} + \frac{9}{76}e^{5} + \frac{79}{76}e^{3} - \frac{193}{38}e$ |
7 | $[7, 7, -w + 11]$ | $-\frac{3}{76}e^{6} + \frac{65}{76}e^{4} - \frac{333}{76}e^{2} + \frac{62}{19}$ |
7 | $[7, 7, w + 11]$ | $\phantom{-}\frac{2}{19}e^{6} - \frac{37}{19}e^{4} + \frac{146}{19}e^{2} - \frac{83}{19}$ |
11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{5}{76}e^{7} - \frac{83}{76}e^{5} + \frac{251}{76}e^{3} - \frac{40}{19}e$ |
11 | $[11, 11, w + 9]$ | $-\frac{21}{152}e^{7} + \frac{379}{152}e^{5} - \frac{1495}{152}e^{3} + \frac{179}{19}e$ |
13 | $[13, 13, w + 6]$ | $\phantom{-}\frac{1}{38}e^{6} - \frac{9}{38}e^{4} - \frac{79}{38}e^{2} + \frac{117}{19}$ |
13 | $[13, 13, w + 7]$ | $-\frac{3}{19}e^{6} + \frac{46}{19}e^{4} - \frac{86}{19}e^{2} - \frac{56}{19}$ |
19 | $[19, 19, w]$ | $-\frac{5}{38}e^{6} + \frac{83}{38}e^{4} - \frac{251}{38}e^{2} + \frac{23}{19}$ |
37 | $[37, 37, w + 15]$ | $-\frac{17}{76}e^{6} + \frac{267}{76}e^{4} - \frac{595}{76}e^{2} - \frac{111}{19}$ |
37 | $[37, 37, w + 22]$ | $-\frac{3}{76}e^{6} + \frac{65}{76}e^{4} - \frac{409}{76}e^{2} + \frac{62}{19}$ |
41 | $[41, 41, 37w + 395]$ | $-\frac{15}{152}e^{7} + \frac{249}{152}e^{5} - \frac{829}{152}e^{3} + \frac{174}{19}e$ |
41 | $[41, 41, 5w + 53]$ | $\phantom{-}\frac{37}{76}e^{7} - \frac{675}{76}e^{5} + \frac{2739}{76}e^{3} - \frac{714}{19}e$ |
67 | $[67, 67, w + 28]$ | $\phantom{-}\frac{4}{19}e^{6} - \frac{74}{19}e^{4} + \frac{311}{19}e^{2} - \frac{318}{19}$ |
67 | $[67, 67, w + 39]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{15}{4}e^{4} + \frac{27}{4}e^{2}$ |
71 | $[71, 71, 40w + 427]$ | $\phantom{-}\frac{5}{38}e^{7} - \frac{32}{19}e^{5} - \frac{36}{19}e^{3} + \frac{809}{38}e$ |
71 | $[71, 71, 8w + 85]$ | $-\frac{17}{152}e^{7} + \frac{343}{152}e^{5} - \frac{1811}{152}e^{3} + \frac{277}{19}e$ |
73 | $[73, 73, -2w + 23]$ | $-\frac{8}{19}e^{6} + \frac{129}{19}e^{4} - \frac{337}{19}e^{2} + \frac{47}{19}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $-1$ |