Properties

Label 4.4.4525.1-41.2-a
Base field 4.4.4525.1
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41,41,\frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{7}{3}w + 3]$
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: $[41,41,\frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{7}{3}w + 3]$
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:

\(x^{4} + 2x^{3} - 15x^{2} - 28x - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}\frac{1}{6}e^{3} - 3e - \frac{13}{6}$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $\phantom{-}e$
9 $[9, 3, -w]$ $-e - 1$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $-\frac{1}{3}e^{3} - \frac{1}{2}e^{2} + \frac{11}{2}e + \frac{29}{6}$
16 $[16, 2, 2]$ $-\frac{1}{3}e^{3} + 4e - \frac{5}{3}$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{15}{2}e - 7$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - 5e - \frac{10}{3}$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{5}{2}e - \frac{17}{3}$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $-\frac{2}{3}e^{3} - \frac{1}{2}e^{2} + \frac{19}{2}e + \frac{31}{6}$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - \frac{9}{2}$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $\phantom{-}1$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $\phantom{-}\frac{1}{6}e^{3} - e + \frac{47}{6}$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{3}{2}e - \frac{29}{3}$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $-\frac{1}{6}e^{3} - e^{2} + 2e + \frac{13}{6}$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{13}{2}e + 2$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}\frac{2}{3}e^{3} + e^{2} - 9e - \frac{44}{3}$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-\frac{3}{2}e^{3} - e^{2} + 23e + \frac{37}{2}$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $\phantom{-}\frac{5}{6}e^{3} + e^{2} - 10e - \frac{53}{6}$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - \frac{23}{2}$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $-\frac{1}{2}e^{3} - e^{2} + 5e + \frac{9}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41,41,\frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{7}{3}w + 3]$ $-1$