Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ |
Dimension: | $6$ |
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:
\(x^{6} - 19x^{4} + 116x^{2} - 225\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $\phantom{-}\frac{1}{15}e^{5} - \frac{4}{15}e^{3} - \frac{19}{15}e$ |
11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $-1$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}\frac{4}{15}e^{5} - \frac{46}{15}e^{3} + \frac{134}{15}e$ |
13 | $[13, 13, -w + 2]$ | $\phantom{-}e^{4} - 13e^{2} + 41$ |
17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{2}{3}e^{5} + \frac{26}{3}e^{3} - \frac{82}{3}e$ |
19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}e^{4} - 12e^{2} + 34$ |
19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $-\frac{13}{15}e^{5} + \frac{157}{15}e^{3} - \frac{443}{15}e$ |
23 | $[23, 23, w^{2} - 2w - 1]$ | $-\frac{11}{15}e^{5} + \frac{149}{15}e^{3} - \frac{481}{15}e$ |
27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{4}{15}e^{5} + \frac{46}{15}e^{3} - \frac{104}{15}e$ |
29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}\frac{2}{3}e^{5} - \frac{26}{3}e^{3} + \frac{79}{3}e$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $-\frac{2}{15}e^{5} + \frac{38}{15}e^{3} - \frac{172}{15}e$ |
41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $-\frac{16}{15}e^{5} + \frac{169}{15}e^{3} - \frac{371}{15}e$ |
53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $-e^{4} + 8e^{2} - 6$ |
59 | $[59, 59, w - 4]$ | $-2e^{4} + 29e^{2} - 96$ |
67 | $[67, 67, 2w^{2} - 3w - 8]$ | $\phantom{-}8$ |
73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $\phantom{-}\frac{14}{15}e^{5} - \frac{206}{15}e^{3} + \frac{694}{15}e$ |
89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $-\frac{28}{15}e^{5} + \frac{352}{15}e^{3} - \frac{1028}{15}e$ |
97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $\phantom{-}e^{4} - 13e^{2} + 37$ |
97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $\phantom{-}\frac{22}{15}e^{5} - \frac{238}{15}e^{3} + \frac{542}{15}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $1$ |