Properties

Label 4.4.9225.1-36.1-h
Base field 4.4.9225.1
Weight $[2, 2, 2, 2]$
Level norm $36$
Level $[36, 6, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{11}{4}]$
Dimension $3$
CM no
Base change no

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Base field 4.4.9225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 10x^{2} + 7x + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[36, 6, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{11}{4}]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + x^{2} - 12x - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ $-1$
4 $[4, 2, \frac{1}{2}w^{3} - 4w - \frac{1}{2}]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ $-1$
11 $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{7}{4}]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 7$
11 $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{3}{2}]$ $\phantom{-}e + 1$
19 $[19, 19, w]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 7$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{5}{2}w + \frac{1}{4}]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 2$
25 $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 5$
29 $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ $-\frac{1}{2}e^{2} + \frac{5}{2}e + 3$
29 $[29, 29, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{9}{2}]$ $-e^{2} + e + 12$
41 $[41, 41, -w^{3} + 7w + 3]$ $-\frac{1}{2}e^{2} + \frac{3}{2}e + 6$
41 $[41, 41, -\frac{3}{4}w^{3} + \frac{11}{2}w - \frac{3}{4}]$ $\phantom{-}e^{2} - 3e - 14$
41 $[41, 41, \frac{1}{4}w^{3} + w^{2} - \frac{5}{2}w - \frac{11}{4}]$ $\phantom{-}e^{2} - 7$
71 $[71, 71, \frac{1}{2}w^{3} - 4w + \frac{5}{2}]$ $\phantom{-}\frac{5}{2}e^{2} - \frac{3}{2}e - 18$
71 $[71, 71, \frac{3}{4}w^{3} + w^{2} - \frac{11}{2}w - \frac{21}{4}]$ $-e^{2} + 17$
79 $[79, 79, \frac{1}{4}w^{3} - 2w^{2} + \frac{1}{2}w + \frac{25}{4}]$ $-e^{2} + e - 2$
79 $[79, 79, -\frac{3}{4}w^{3} + \frac{13}{2}w + \frac{9}{4}]$ $\phantom{-}e^{2} + e - 4$
89 $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{41}{4}]$ $-\frac{5}{2}e^{2} + \frac{1}{2}e + 19$
89 $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{33}{4}]$ $\phantom{-}\frac{5}{2}e^{2} - \frac{3}{2}e - 20$
101 $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{1}{2}w - \frac{27}{4}]$ $-3e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ $1$
$9$ $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ $1$