Properties

Label 4.4.19225.1-9.1-d
Base field 4.4.19225.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$
Dimension $3$
CM no
Base change no

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Base field 4.4.19225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $17$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - 9x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - \frac{11}{3}$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}1$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $-\frac{2}{3}e^{2} + \frac{1}{3}e + \frac{7}{3}$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-\frac{1}{3}e^{2} - \frac{1}{3}e - \frac{1}{3}$
11 $[11, 11, -w - 3]$ $-\frac{2}{3}e^{2} + \frac{4}{3}e + \frac{10}{3}$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-\frac{2}{3}e^{2} - \frac{2}{3}e + \frac{1}{3}$
29 $[29, 29, w + 1]$ $-\frac{1}{3}e^{2} + \frac{2}{3}e - \frac{13}{3}$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $-e^{2} - 2e + 9$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{4}{3}e - \frac{8}{3}$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $\phantom{-}\frac{4}{3}e^{2} - \frac{2}{3}e - \frac{20}{3}$
31 $[31, 31, -w + 3]$ $\phantom{-}e^{2} - 2e - 9$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $\phantom{-}e^{2} + e - 4$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}2e^{2} - 5$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}e + 8$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $-3e - 1$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e + \frac{4}{3}$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $-\frac{1}{3}e^{2} + \frac{11}{3}e + \frac{14}{3}$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - \frac{8}{3}$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $-\frac{4}{3}e^{2} - \frac{7}{3}e + \frac{50}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $-1$