Properties

Base field 4.4.13888.1
Weight [2, 2, 2, 2]
Level norm 4
Level $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$
Label 4.4.13888.1-4.1-a
Dimension 4
CM no
Base change yes

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Base field 4.4.13888.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 6x + 9\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$
Label 4.4.13888.1-4.1-a
Dimension 4
Is CM no
Is base change yes
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 34x^{2} \) \(\mathstrut +\mathstrut 200\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $-1$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}\frac{1}{20}e^{3} - \frac{7}{10}e$
7 $[7, 7, w - 2]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{1}{20}e^{3} - \frac{7}{10}e$
9 $[9, 3, w]$ $\phantom{-}0$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $\phantom{-}0$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $-\frac{1}{2}e^{2} + 11$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $-\frac{1}{2}e^{2} + 11$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $-e^{2} + 16$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $-\frac{1}{5}e^{3} + \frac{29}{5}e$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $-\frac{1}{5}e^{3} + \frac{29}{5}e$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $\phantom{-}\frac{1}{10}e^{3} - \frac{12}{5}e$
47 $[47, 47, w^{2} - w - 4]$ $\phantom{-}\frac{1}{10}e^{3} - \frac{12}{5}e$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $-\frac{1}{5}e^{3} + \frac{24}{5}e$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $-e^{2} + 18$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-e^{2} + 18$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $-\frac{1}{5}e^{3} + \frac{24}{5}e$
79 $[79, 79, w^{2} - 5]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{43}{5}e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{43}{5}e$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $-\frac{3}{20}e^{3} + \frac{11}{10}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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