Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 18
Level $[18,6,w - 2]$
Label 4.4.18688.1-18.2-a
Dimension 6
CM no
Base change no

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Base field 4.4.18688.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[18,6,w - 2]$
Label 4.4.18688.1-18.2-a
Dimension 6
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:
\(x^{6} \) \(\mathstrut -\mathstrut 4x^{5} \) \(\mathstrut -\mathstrut 5x^{4} \) \(\mathstrut +\mathstrut 25x^{3} \) \(\mathstrut -\mathstrut 5x^{2} \) \(\mathstrut -\mathstrut 17x \) \(\mathstrut -\mathstrut 3\)

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Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $-\frac{1}{2}e^{5} + \frac{5}{2}e^{4} + e^{3} - \frac{31}{2}e^{2} + 10e + \frac{15}{2}$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $-\frac{1}{2}e^{5} + \frac{5}{2}e^{4} + e^{3} - \frac{31}{2}e^{2} + 10e + \frac{13}{2}$
9 $[9, 3, w + 1]$ $-1$
17 $[17, 17, w + 3]$ $\phantom{-}2e - 3$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $\phantom{-}e^{5} - 4e^{4} - 4e^{3} + 23e^{2} - 12e - 9$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $\phantom{-}e^{5} - 3e^{4} - 7e^{3} + 15e^{2} + 2e$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $\phantom{-}2e^{5} - 7e^{4} - 11e^{3} + 38e^{2} - 9e - 9$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $-e^{3} + 2e^{2} + 5e - 6$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}e^{5} - 3e^{4} - 7e^{3} + 16e^{2} + 2e - 9$
41 $[41, 41, 2w + 3]$ $\phantom{-}e^{5} - 4e^{4} - 4e^{3} + 23e^{2} - 15e - 9$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $-e^{5} + 6e^{4} - e^{3} - 39e^{2} + 36e + 21$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $-2e^{5} + 7e^{4} + 11e^{3} - 38e^{2} + 9e + 9$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-\frac{1}{2}e^{5} + \frac{3}{2}e^{4} + 4e^{3} - \frac{15}{2}e^{2} - 7e + \frac{3}{2}$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $-\frac{1}{2}e^{5} + \frac{7}{2}e^{4} - 2e^{3} - \frac{47}{2}e^{2} + 26e + \frac{25}{2}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $-\frac{1}{2}e^{5} + \frac{7}{2}e^{4} - 3e^{3} - \frac{43}{2}e^{2} + 31e + \frac{17}{2}$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $-\frac{5}{2}e^{5} + \frac{17}{2}e^{4} + 15e^{3} - \frac{91}{2}e^{2} + 4e + \frac{17}{2}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $-\frac{3}{2}e^{5} + \frac{9}{2}e^{4} + 11e^{3} - \frac{51}{2}e^{2} - 5e + \frac{17}{2}$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $-e^{5} + 6e^{4} - e^{3} - 38e^{2} + 36e + 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{8}{3}]$ $1$
9 $[9,3,-w - 1]$ $1$