Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7, 7, w - 2]$ |
Dimension: | $10$ |
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:
\(x^{10} - 18x^{8} + 92x^{6} - 132x^{4} + 60x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $-\frac{3}{4}e^{9} + \frac{53}{4}e^{7} - \frac{129}{2}e^{5} + \frac{153}{2}e^{3} - 17e$ |
5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{9}{2}e^{7} + 23e^{5} - 33e^{3} + 14e$ |
7 | $[7, 7, w - 2]$ | $-1$ |
11 | $[11, 11, w^{2} - 2w - 4]$ | $-\frac{3}{4}e^{8} + 13e^{6} - \frac{121}{2}e^{4} + 61e^{2} - 10$ |
23 | $[23, 23, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{3}{4}e^{9} - \frac{27}{2}e^{7} + 69e^{5} - 98e^{3} + 37e$ |
23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{1}{4}e^{9} + \frac{9}{2}e^{7} - 23e^{5} + 32e^{3} - 5e$ |
27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}\frac{11}{4}e^{9} - \frac{97}{2}e^{7} + \frac{471}{2}e^{5} - 280e^{3} + 74e$ |
31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $\phantom{-}\frac{3}{4}e^{8} - \frac{27}{2}e^{6} + \frac{137}{2}e^{4} - 92e^{2} + 28$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}2e^{9} - \frac{71}{2}e^{7} + 175e^{5} - 219e^{3} + 63e$ |
37 | $[37, 37, w^{2} - 2w - 6]$ | $-\frac{3}{4}e^{8} + \frac{27}{2}e^{6} - \frac{137}{2}e^{4} + 92e^{2} - 24$ |
37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}3e^{9} - 53e^{7} + \frac{517}{2}e^{5} - 312e^{3} + 83e$ |
43 | $[43, 43, w^{2} - 3w - 2]$ | $-\frac{9}{4}e^{9} + 40e^{7} - 198e^{5} + 251e^{3} - 73e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{5}{4}e^{9} - 22e^{7} + 106e^{5} - 121e^{3} + 27e$ |
73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $\phantom{-}\frac{3}{2}e^{9} - 26e^{7} + 121e^{5} - 122e^{3} + 22e$ |
83 | $[83, 83, -w - 3]$ | $\phantom{-}2e^{2} - 10$ |
89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{2}e^{9} - 8e^{7} + 29e^{5} + 10e^{3} - 36e$ |
89 | $[89, 89, 2w - 1]$ | $\phantom{-}\frac{3}{4}e^{9} - \frac{27}{2}e^{7} + 69e^{5} - 98e^{3} + 39e$ |
101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $\phantom{-}2e^{8} - 35e^{6} + 167e^{4} - 186e^{2} + 42$ |
101 | $[101, 101, 2w^{2} - 3w - 3]$ | $\phantom{-}\frac{23}{4}e^{9} - \frac{203}{2}e^{7} + 494e^{5} - 591e^{3} + 152e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, w - 2]$ | $1$ |