Base field 4.4.16357.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[15, 15, -w^{3} + 6w - 1]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} - 8x^{6} + 8x^{5} + 68x^{4} - 140x^{3} - 64x^{2} + 176x + 48\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $-1$ |
5 | $[5, 5, -w^{3} + 5w + 2]$ | $-1$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{3} + 5w]$ | $-\frac{1}{8}e^{6} + \frac{3}{4}e^{5} + \frac{1}{4}e^{4} - \frac{13}{2}e^{3} + 5e^{2} + 5e$ |
13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - e^{4} - 2e^{3} + 8e^{2} + e - 4$ |
16 | $[16, 2, 2]$ | $-\frac{1}{8}e^{6} + \frac{5}{8}e^{5} + \frac{3}{4}e^{4} - \frac{23}{4}e^{3} + \frac{1}{2}e^{2} + 9e + 4$ |
19 | $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ | $-\frac{1}{4}e^{6} + \frac{3}{2}e^{5} + \frac{1}{2}e^{4} - \frac{27}{2}e^{3} + 10e^{2} + 16e - 2$ |
25 | $[25, 5, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + 5e^{2} - 9e - 10$ |
27 | $[27, 3, w^{3} - w^{2} - 5w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 4e + 2$ |
31 | $[31, 31, -w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 3e + 4$ |
37 | $[37, 37, -w^{3} - w^{2} + 6w + 4]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{3}{4}e^{5} - \frac{1}{4}e^{4} + \frac{13}{2}e^{3} - 5e^{2} - 5e + 2$ |
41 | $[41, 41, w^{3} + w^{2} - 6w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 6e^{2} + 8e + 6$ |
43 | $[43, 43, w^{3} - 7w - 2]$ | $-\frac{1}{4}e^{6} + \frac{7}{4}e^{5} - \frac{1}{2}e^{4} - \frac{31}{2}e^{3} + 19e^{2} + 16e - 10$ |
47 | $[47, 47, -2w^{3} + 11w + 2]$ | $-\frac{1}{4}e^{6} + \frac{5}{4}e^{5} + 2e^{4} - 13e^{3} - 2e^{2} + 25e + 6$ |
61 | $[61, 61, w^{2} - 3]$ | $-\frac{1}{4}e^{5} + \frac{1}{2}e^{4} + 4e^{3} - 5e^{2} - 13e + 4$ |
67 | $[67, 67, w^{2} + w - 4]$ | $-\frac{1}{2}e^{4} + 2e^{3} + 5e^{2} - 16e - 8$ |
79 | $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{4}e^{5} - 2e^{4} + \frac{25}{2}e^{3} + 3e^{2} - 20e - 14$ |
97 | $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{3}{2}e^{5} - \frac{1}{2}e^{4} + \frac{27}{2}e^{3} - 9e^{2} - 17e - 2$ |
97 | $[97, 97, -w^{3} + 6w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{7}{2}e^{3} + 4e^{2} + 12e - 8$ |
97 | $[97, 97, -3w^{3} + 16w]$ | $-\frac{1}{8}e^{6} + e^{5} - \frac{5}{4}e^{4} - 8e^{3} + 20e^{2} + 5e - 16$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $1$ |
$5$ | $[5, 5, -w^{3} + 5w + 2]$ | $1$ |