Base field 4.4.13888.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 6x + 9\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 34x^{8} + 385x^{6} - 1640x^{4} + 1928x^{2} - 576\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ | $\phantom{-}\frac{1}{1012}e^{8} - \frac{3}{88}e^{6} + \frac{931}{2024}e^{4} - \frac{67}{23}e^{2} + \frac{1230}{253}$ |
7 | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w - 2]$ | $\phantom{-}\frac{7}{1012}e^{9} - \frac{21}{88}e^{7} + \frac{5505}{2024}e^{5} - \frac{501}{46}e^{3} + \frac{1526}{253}e$ |
7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{109}{6072}e^{9} - \frac{79}{132}e^{7} + \frac{39481}{6072}e^{5} - \frac{3439}{138}e^{3} + \frac{13399}{759}e$ |
9 | $[9, 3, w]$ | $\phantom{-}\frac{73}{12144}e^{9} - \frac{13}{66}e^{7} + \frac{25759}{12144}e^{5} - \frac{1169}{138}e^{3} + \frac{14029}{1518}e$ |
9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ | $\phantom{-}\frac{1}{1104}e^{9} - \frac{1}{24}e^{7} + \frac{661}{1104}e^{5} - \frac{167}{69}e^{3} - \frac{305}{138}e$ |
23 | $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ | $-\frac{15}{2024}e^{8} + \frac{17}{88}e^{6} - \frac{351}{253}e^{4} + \frac{54}{23}e^{2} + \frac{136}{253}$ |
23 | $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ | $-1$ |
31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ | $-\frac{27}{1012}e^{8} + \frac{35}{44}e^{6} - \frac{3691}{506}e^{4} + \frac{498}{23}e^{2} - \frac{2344}{253}$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ | $-\frac{73}{4048}e^{9} + \frac{13}{22}e^{7} - \frac{25759}{4048}e^{5} + \frac{1169}{46}e^{3} - \frac{13017}{506}e$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ | $-\frac{475}{12144}e^{9} + \frac{337}{264}e^{7} - \frac{163555}{12144}e^{5} + \frac{6839}{138}e^{3} - \frac{48739}{1518}e$ |
47 | $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ | $-\frac{7}{759}e^{9} + \frac{73}{264}e^{7} - \frac{15695}{6072}e^{5} + \frac{565}{69}e^{3} - \frac{5345}{759}e$ |
47 | $[47, 47, w^{2} - w - 4]$ | $-\frac{3}{506}e^{9} + \frac{9}{44}e^{7} - \frac{2287}{1012}e^{5} + \frac{367}{46}e^{3} - \frac{43}{253}e$ |
73 | $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ | $-\frac{397}{12144}e^{9} + \frac{295}{264}e^{7} - \frac{152293}{12144}e^{5} + \frac{6917}{138}e^{3} - \frac{61489}{1518}e$ |
73 | $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ | $-\frac{14}{253}e^{8} + \frac{73}{44}e^{6} - \frac{15695}{1012}e^{4} + \frac{1130}{23}e^{2} - \frac{9172}{253}$ |
73 | $[73, 73, -w^{3} + w^{2} + 7w + 1]$ | $-\frac{51}{2024}e^{8} + \frac{71}{88}e^{6} - \frac{8771}{1012}e^{4} + \frac{800}{23}e^{2} - \frac{5812}{253}$ |
73 | $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ | $\phantom{-}\frac{67}{4048}e^{9} - \frac{53}{88}e^{7} + \frac{29291}{4048}e^{5} - \frac{691}{23}e^{3} + \frac{8821}{506}e$ |
79 | $[79, 79, w^{2} - 5]$ | $\phantom{-}\frac{13}{1012}e^{9} - \frac{39}{88}e^{7} + \frac{10079}{2024}e^{5} - \frac{434}{23}e^{3} + \frac{2075}{253}e$ |
79 | $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ | $\phantom{-}\frac{13}{759}e^{9} - \frac{145}{264}e^{7} + \frac{35003}{6072}e^{5} - \frac{3035}{138}e^{3} + \frac{13613}{759}e$ |
97 | $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ | $-\frac{9}{368}e^{9} + \frac{7}{8}e^{7} - \frac{3833}{368}e^{5} + \frac{2063}{46}e^{3} - \frac{1809}{46}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ | $1$ |