Properties

Label 4.4.5125.1-41.1-i
Base field 4.4.5125.1
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, 3w^{2} - 2w - 10]$
Dimension $4$
CM no
Base change no

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Base field 4.4.5125.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 7x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[41, 41, 3w^{2} - 2w - 10]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 76x^{2} + 1280\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $-\frac{1}{4}e^{2} + 10$
9 $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ $\phantom{-}0$
9 $[9, 3, -w^{3} + 5w + 5]$ $\phantom{-}0$
11 $[11, 11, w]$ $-\frac{1}{4}e^{2} + 8$
11 $[11, 11, w - 1]$ $-\frac{1}{4}e^{2} + 8$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{4}e^{2} - 7$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e$
19 $[19, 19, w^{3} - w^{2} - 4w + 2]$ $-e$
29 $[29, 29, w^{3} - 4w^{2} - w + 10]$ $-e$
29 $[29, 29, -w^{3} + 3w^{2} + w - 7]$ $\phantom{-}e$
41 $[41, 41, 3w^{2} - 2w - 10]$ $-1$
49 $[49, 7, -2w^{2} + 3w + 8]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{9}{2}e$
49 $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ $-\frac{1}{8}e^{3} + \frac{9}{2}e$
71 $[71, 71, -w - 3]$ $-\frac{1}{4}e^{2} + 12$
71 $[71, 71, w - 4]$ $-\frac{1}{4}e^{2} + 12$
79 $[79, 79, -w^{3} + w^{2} + 3w + 3]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{11}{2}e$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $-\frac{1}{8}e^{3} + \frac{11}{2}e$
89 $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ $-\frac{1}{8}e^{3} + \frac{11}{2}e$
89 $[89, 89, w^{3} - 6w - 2]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{11}{2}e$
101 $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ $\phantom{-}\frac{3}{4}e^{2} - 22$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, 3w^{2} - 2w - 10]$ $1$