Properties

Label 5.5.89417.1-41.2-c
Base field 5.5.89417.1
Weight $[2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, -w^{3} + 2w + 2]$
Dimension $4$
CM no
Base change no

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Base field 5.5.89417.1

Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} - x^{2} + 8x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[41, 41, -w^{3} + 2w + 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 8x^{2} + 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{2} - 3]$ $\phantom{-}e$
5 $[5, 5, w^{4} - 5w^{2} + 4]$ $\phantom{-}\frac{1}{2}e^{3} - 3e$
11 $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ $-\frac{1}{2}e^{2}$
17 $[17, 17, w^{4} - 4w^{2} + 2]$ $-e^{2}$
32 $[32, 2, 2]$ $-\frac{3}{2}e^{2} + 3$
37 $[37, 37, -w^{4} + 2w^{3} + 5w^{2} - 7w - 5]$ $-\frac{1}{4}e^{3} + e$
37 $[37, 37, -w^{3} + 4w - 1]$ $-\frac{3}{2}e^{3} + 7e$
41 $[41, 41, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}e^{3} - 6e$
41 $[41, 41, -w^{3} + 2w + 2]$ $-1$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}e^{3} - 8e$
49 $[49, 7, w^{4} - 5w^{2} + 2]$ $-2e^{3} + 11e$
53 $[53, 53, w^{4} - w^{3} - 5w^{2} + 2w + 5]$ $\phantom{-}e^{2} - 12$
59 $[59, 59, w^{4} - w^{3} - 4w^{2} + 3w - 1]$ $\phantom{-}2e^{2} - 12$
67 $[67, 67, -w^{4} + 3w^{2} + 2w + 2]$ $-\frac{3}{4}e^{3} + 8e$
79 $[79, 79, w^{3} - w^{2} - 4w + 2]$ $-3e^{2} + 16$
81 $[81, 3, -w^{4} + 6w^{2} + w - 8]$ $\phantom{-}\frac{1}{2}e^{3} - 3e$
83 $[83, 83, w^{4} + w^{3} - 5w^{2} - 4w + 1]$ $\phantom{-}\frac{3}{4}e^{3} - 4e$
89 $[89, 89, -w^{4} + 5w^{2} + w - 1]$ $\phantom{-}\frac{3}{4}e^{3} - 7e$
97 $[97, 97, -w^{4} + 2w^{3} + 5w^{2} - 5w - 5]$ $\phantom{-}\frac{3}{2}e^{2} - 4$
101 $[101, 101, 2w^{2} - w - 2]$ $\phantom{-}\frac{3}{4}e^{3} - 5e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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