Base field 4.4.10304.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 8\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 17x^{8} + 101x^{6} - 251x^{4} + 230x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 2]$ | $\phantom{-}e$ |
2 | $[2, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 1]$ | $-\frac{1}{8}e^{9} + \frac{15}{8}e^{7} - \frac{73}{8}e^{5} + \frac{133}{8}e^{3} - \frac{37}{4}e$ |
7 | $[7, 7, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + w - 3]$ | $-\frac{1}{4}e^{7} + 3e^{5} - \frac{37}{4}e^{3} + \frac{11}{2}e$ |
23 | $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ | $-1$ |
25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{9}{2}w + 1]$ | $\phantom{-}e^{3} - 7e$ |
25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{5}{2}w - 1]$ | $-\frac{1}{2}e^{9} + \frac{15}{2}e^{7} - \frac{73}{2}e^{5} + \frac{131}{2}e^{3} - 32e$ |
31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 1]$ | $-\frac{1}{4}e^{9} + \frac{15}{4}e^{7} - \frac{73}{4}e^{5} + \frac{133}{4}e^{3} - \frac{37}{2}e$ |
31 | $[31, 31, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w + 1]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{15}{4}e^{7} + \frac{69}{4}e^{5} - \frac{93}{4}e^{3} - \frac{3}{2}e$ |
41 | $[41, 41, \frac{3}{2}w^{3} - w^{2} - \frac{21}{2}w - 5]$ | $\phantom{-}\frac{1}{2}e^{7} - 7e^{5} + \frac{57}{2}e^{3} - 30e$ |
41 | $[41, 41, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 7]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{15}{4}e^{7} + \frac{73}{4}e^{5} - \frac{133}{4}e^{3} + \frac{43}{2}e$ |
47 | $[47, 47, -w^{2} - w + 5]$ | $\phantom{-}\frac{1}{2}e^{8} - 7e^{6} + \frac{59}{2}e^{4} - 35e^{2} - 8$ |
47 | $[47, 47, -w^{3} + \frac{1}{2}w^{2} + \frac{13}{2}w + 5]$ | $-\frac{1}{2}e^{8} + 7e^{6} - \frac{61}{2}e^{4} + 45e^{2} - 8$ |
49 | $[49, 7, \frac{1}{2}w^{2} - \frac{1}{2}w - 5]$ | $-\frac{1}{4}e^{8} + 3e^{6} - \frac{37}{4}e^{4} + \frac{3}{2}e^{2} + 12$ |
73 | $[73, 73, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $\phantom{-}e^{5} - 10e^{3} + 21e$ |
73 | $[73, 73, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 1]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{15}{4}e^{7} + \frac{73}{4}e^{5} - \frac{121}{4}e^{3} + \frac{7}{2}e$ |
79 | $[79, 79, w^{2} - 3w + 1]$ | $-\frac{1}{4}e^{9} + \frac{13}{4}e^{7} - \frac{49}{4}e^{5} + \frac{51}{4}e^{3} + \frac{1}{2}e$ |
79 | $[79, 79, w^{2} + w - 1]$ | $-\frac{1}{4}e^{9} + \frac{13}{4}e^{7} - \frac{49}{4}e^{5} + \frac{55}{4}e^{3} - \frac{11}{2}e$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{2}e^{8} - 7e^{6} + \frac{59}{2}e^{4} - 35e^{2} - 10$ |
89 | $[89, 89, -\frac{1}{2}w^{3} + 3w^{2} + \frac{7}{2}w - 11]$ | $-\frac{1}{4}e^{9} + \frac{5}{2}e^{7} - \frac{13}{4}e^{5} - 16e^{3} + 20e$ |
89 | $[89, 89, \frac{1}{2}w^{3} - \frac{5}{2}w - 3]$ | $\phantom{-}\frac{3}{4}e^{8} - 10e^{6} + \frac{159}{4}e^{4} - \frac{99}{2}e^{2} + 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ | $1$ |