Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 9
Level $[9,3,-w - 1]$
Label 4.4.18688.1-9.2-b
Dimension 3
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 $[9,3,-w - 1]$
Label 4.4.18688.1-9.2-b
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 22

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut +\mathstrut x^{2} \) \(\mathstrut -\mathstrut 10x \) \(\mathstrut +\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}1$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 3$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 5$
9 $[9, 3, w + 1]$ $\phantom{-}1$
17 $[17, 17, w + 3]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 4$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $-e^{2} - 2e + 6$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 4$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $\phantom{-}e^{2} + e - 6$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}2e - 2$
41 $[41, 41, 2w + 3]$ $\phantom{-}2e^{2} + 4e - 14$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $-\frac{1}{2}e^{2} + \frac{3}{2}e + 3$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 3$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 4$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $-e^{2} - 3e + 2$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $-\frac{3}{2}e^{2} - \frac{9}{2}e + 8$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $-\frac{3}{2}e^{2} + \frac{1}{2}e + 9$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $-e^{2} - e$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $\phantom{-}\frac{3}{2}e^{2} + \frac{3}{2}e - 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9,3,-w - 1]$ $-1$