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-e
Dimension 8
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-e
Dimension 8
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:
\(x^{8} \) \(\mathstrut -\mathstrut 18x^{6} \) \(\mathstrut +\mathstrut 71x^{4} \) \(\mathstrut -\mathstrut 80x^{2} \) \(\mathstrut +\mathstrut 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $-\frac{5}{66}e^{6} + \frac{38}{33}e^{4} - \frac{43}{22}e^{2} - \frac{7}{33}$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 2]$ $-\frac{13}{66}e^{7} + \frac{112}{33}e^{5} - \frac{257}{22}e^{3} + \frac{391}{33}e$
7 $[7, 7, w - 1]$ $-\frac{2}{11}e^{7} + \frac{37}{11}e^{5} - \frac{155}{11}e^{3} + \frac{166}{11}e$
9 $[9, 3, w]$ $\phantom{-}\frac{29}{132}e^{7} - \frac{227}{66}e^{5} + \frac{333}{44}e^{3} + \frac{17}{33}e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $\phantom{-}0$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $-\frac{1}{66}e^{6} + \frac{1}{33}e^{4} + \frac{31}{22}e^{2} + \frac{58}{33}$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $-1$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $-\frac{19}{66}e^{6} + \frac{151}{33}e^{4} - \frac{247}{22}e^{2} + \frac{112}{33}$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $-\frac{8}{33}e^{7} + \frac{148}{33}e^{5} - \frac{203}{11}e^{3} + \frac{532}{33}e$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $-\frac{79}{132}e^{7} + \frac{673}{66}e^{5} - \frac{1467}{44}e^{3} + \frac{971}{33}e$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $\phantom{-}\frac{31}{132}e^{7} - \frac{229}{66}e^{5} + \frac{227}{44}e^{3} + \frac{157}{33}e$
47 $[47, 47, w^{2} - w - 4]$ $-\frac{13}{44}e^{7} + \frac{123}{22}e^{5} - \frac{1123}{44}e^{3} + \frac{377}{11}e$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $\phantom{-}\frac{8}{33}e^{7} - \frac{115}{33}e^{5} + \frac{38}{11}e^{3} + \frac{425}{33}e$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $-\frac{1}{11}e^{6} + \frac{13}{11}e^{4} - \frac{17}{11}e^{2} + \frac{116}{11}$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $\phantom{-}\frac{2}{11}e^{6} - \frac{37}{11}e^{4} + \frac{166}{11}e^{2} - \frac{144}{11}$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $-\frac{13}{33}e^{7} + \frac{224}{33}e^{5} - \frac{257}{11}e^{3} + \frac{650}{33}e$
79 $[79, 79, w^{2} - 5]$ $\phantom{-}\frac{35}{132}e^{7} - \frac{299}{66}e^{5} + \frac{631}{44}e^{3} - \frac{124}{33}e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $-\frac{1}{11}e^{7} + \frac{13}{11}e^{5} + \frac{5}{11}e^{3} - \frac{60}{11}e$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $-\frac{1}{2}e^{7} + 8e^{5} - \frac{39}{2}e^{3} + 3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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