Properties

Base field 4.4.13888.1
Weight [2, 2, 2, 2]
Level norm 23
Level $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$
Label 4.4.13888.1-23.2-f
Dimension 10
CM no
Base change no

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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 $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$
Label 4.4.13888.1-23.2-f
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 28

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut -\mathstrut 34x^{8} \) \(\mathstrut +\mathstrut 385x^{6} \) \(\mathstrut -\mathstrut 1640x^{4} \) \(\mathstrut +\mathstrut 1928x^{2} \) \(\mathstrut -\mathstrut 576\)

  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 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $-\frac{9}{368}e^{9} + \frac{7}{8}e^{7} - \frac{3833}{368}e^{5} + \frac{2063}{46}e^{3} - \frac{1809}{46}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $1$