Properties

Label 4.4.4525.1-45.4-e
Base field 4.4.4525.1
Weight $[2, 2, 2, 2]$
Level norm $45$
Level $[45,15,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 4]$
Dimension $4$
CM no
Base change no

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Base field 4.4.4525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 3x + 9\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[45,15,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 4]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $11$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - x^{3} - 13x^{2} - 3x + 18\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $-1$
9 $[9, 3, -w]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{7}{3}e + 6$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $-1$
16 $[16, 2, 2]$ $-e^{2} + e + 5$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{1}{3}e + 8$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $-\frac{2}{3}e^{3} + \frac{5}{3}e^{2} + \frac{20}{3}e - 4$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $-e^{3} + 2e^{2} + 8e - 2$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 4$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{2}{3}e^{2} - \frac{20}{3}e - 4$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $-\frac{1}{3}e^{3} - \frac{2}{3}e^{2} + \frac{16}{3}e + 2$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{5}{3}e^{2} - \frac{20}{3}e + 6$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $-\frac{4}{3}e^{3} + \frac{7}{3}e^{2} + \frac{40}{3}e$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{19}{3}e + 10$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-\frac{2}{3}e^{3} + \frac{8}{3}e^{2} + \frac{14}{3}e - 14$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}\frac{2}{3}e^{3} + \frac{1}{3}e^{2} - \frac{26}{3}e - 10$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $\phantom{-}e + 6$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $\phantom{-}e^{3} - 2e^{2} - 11e$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{1}{3}e + 10$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $\phantom{-}e^{3} - e^{2} - 9e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,-\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 3]$ $1$
$9$ $[9,3,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $1$