Properties

Base field 4.4.19225.1
Weight [2, 2, 2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 4.4.19225.1-1.1-b
Dimension 6
CM no
Base change yes

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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 $[1, 1, 1]$
Label 4.4.19225.1-1.1-b
Dimension 6
Is CM no
Is base change yes
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 5x^{5} - x^{4} - 28x^{3} - 15x^{2} + 21x + 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{3}{2}e^{3} - \frac{19}{2}e^{2} - 2e + \frac{5}{2}$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{3}{2}e^{3} - \frac{19}{2}e^{2} - 2e + \frac{5}{2}$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-e^{3} - 2e^{2} + 5e + 4$
11 $[11, 11, -w - 3]$ $-e^{3} - 2e^{2} + 5e + 4$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $\phantom{-}e^{4} + 3e^{3} - 5e^{2} - 13e + 6$
29 $[29, 29, w + 1]$ $-\frac{1}{2}e^{5} - 2e^{4} + \frac{3}{2}e^{3} + \frac{21}{2}e^{2} + 5e - \frac{5}{2}$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $-\frac{1}{2}e^{5} - 2e^{4} + \frac{3}{2}e^{3} + \frac{21}{2}e^{2} + 5e - \frac{5}{2}$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 8e + 4$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-e^{3} - e^{2} + 5e - 1$
31 $[31, 31, -w + 3]$ $-e^{3} - e^{2} + 5e - 1$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 8e + 4$
59 $[59, 59, 2w^{2} - w - 13]$ $-e^{4} - 2e^{3} + 5e^{2} + 4e$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $-e^{4} - 2e^{3} + 5e^{2} + 4e$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{5}{2}e^{3} - \frac{21}{2}e^{2} + 6e + \frac{13}{2}$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{5}{2}e^{3} - \frac{21}{2}e^{2} + 6e + \frac{13}{2}$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $-e^{4} - 3e^{3} + 3e^{2} + 9e + 4$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $-e^{4} - 3e^{3} + 3e^{2} + 9e + 4$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $-e^{5} - 4e^{4} + 3e^{3} + 22e^{2} + 10e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).