Base field 4.4.11197.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{2} + 2w + 2]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} + 4x^{6} - 9x^{5} - 45x^{4} + 5x^{3} + 101x^{2} + 10x - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}\frac{7}{2}e^{6} + 4e^{5} - \frac{85}{2}e^{4} - \frac{71}{2}e^{3} + \frac{229}{2}e^{2} + \frac{45}{2}e - 22$ |
11 | $[11, 11, -w - 2]$ | $-e^{6} - e^{5} + 12e^{4} + 9e^{3} - 32e^{2} - 7e + 8$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ | $-e - 2$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}1$ |
16 | $[16, 2, 2]$ | $\phantom{-}2e^{6} + 2e^{5} - 25e^{4} - 17e^{3} + 71e^{2} + 5e - 13$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $-7e^{6} - 8e^{5} + 85e^{4} + 71e^{3} - 228e^{2} - 45e + 34$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}3e^{6} + 3e^{5} - 37e^{4} - 26e^{3} + 103e^{2} + 12e - 22$ |
23 | $[23, 23, -w^{2} + 3]$ | $-2e^{6} - 2e^{5} + 25e^{4} + 16e^{3} - 72e^{2} + e + 16$ |
27 | $[27, 3, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}\frac{3}{2}e^{6} + e^{5} - \frac{37}{2}e^{4} - \frac{13}{2}e^{3} + \frac{103}{2}e^{2} - \frac{25}{2}e - 8$ |
29 | $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ | $-4e^{6} - 4e^{5} + 49e^{4} + 34e^{3} - 134e^{2} - 10e + 18$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}\frac{3}{2}e^{6} + 2e^{5} - \frac{35}{2}e^{4} - \frac{37}{2}e^{3} + \frac{83}{2}e^{2} + \frac{33}{2}e$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ | $-\frac{5}{2}e^{6} - 2e^{5} + \frac{63}{2}e^{4} + \frac{33}{2}e^{3} - \frac{183}{2}e^{2} - \frac{1}{2}e + 20$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $-\frac{9}{2}e^{6} - 4e^{5} + \frac{111}{2}e^{4} + \frac{65}{2}e^{3} - \frac{309}{2}e^{2} + \frac{1}{2}e + 28$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}\frac{3}{2}e^{6} + e^{5} - \frac{37}{2}e^{4} - \frac{17}{2}e^{3} + \frac{101}{2}e^{2} + \frac{1}{2}e - 6$ |
67 | $[67, 67, -w^{3} + w^{2} + 5w - 1]$ | $\phantom{-}\frac{9}{2}e^{6} + 5e^{5} - \frac{111}{2}e^{4} - \frac{91}{2}e^{3} + \frac{309}{2}e^{2} + \frac{71}{2}e - 36$ |
67 | $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ | $-\frac{7}{2}e^{6} - 4e^{5} + \frac{85}{2}e^{4} + \frac{73}{2}e^{3} - \frac{229}{2}e^{2} - \frac{61}{2}e + 16$ |
83 | $[83, 83, -2w + 3]$ | $\phantom{-}\frac{5}{2}e^{6} + 2e^{5} - \frac{61}{2}e^{4} - \frac{33}{2}e^{3} + \frac{167}{2}e^{2} + \frac{1}{2}e - 16$ |
89 | $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ | $\phantom{-}2e^{6} + 3e^{5} - 24e^{4} - 29e^{3} + 63e^{2} + 38e - 14$ |
97 | $[97, 97, w^{3} - w^{2} - 4w - 3]$ | $-6e^{6} - 7e^{5} + 73e^{4} + 63e^{3} - 197e^{2} - 43e + 34$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{2} + 2w + 2]$ | $-1$ |