Properties

Label 4.4.17417.1-10.1-d
Base field 4.4.17417.1
Weight $[2, 2, 2, 2]$
Level norm $10$
Level $[10, 10, -w^{3} + 3w^{2} + 2w - 6]$
Dimension $5$
CM no
Base change no

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Base field 4.4.17417.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[10, 10, -w^{3} + 3w^{2} + 2w - 6]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 3x^{4} - 11x^{3} + 19x^{2} + 40x + 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 3w^{2} - w + 2]$ $-1$
5 $[5, 5, w^{2} - 2w - 3]$ $-1$
5 $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ $\phantom{-}e$
8 $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{9}{4}e^{2} + \frac{41}{4}e + \frac{15}{2}$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}e^{2} - 2e - 4$
17 $[17, 17, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{5}{2}e^{3} - \frac{5}{2}e^{2} + \frac{31}{2}e + 9$
23 $[23, 23, w^{2} - 3]$ $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{9}{2}e^{2} - \frac{19}{2}e - 9$
25 $[25, 5, -w^{2} + 2w + 1]$ $\phantom{-}2e - 4$
37 $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ $-e^{3} + 2e^{2} + 7e - 4$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{5}{2}e^{2} + \frac{11}{2}e - 3$
49 $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ $\phantom{-}e^{3} - 3e^{2} - 5e + 8$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 15e + 8$
59 $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ $\phantom{-}e^{4} - 3e^{3} - 8e^{2} + 15e + 18$
67 $[67, 67, -w^{3} + 3w^{2} + w - 5]$ $\phantom{-}e^{3} - 4e^{2} - 3e + 14$
71 $[71, 71, 2w - 3]$ $\phantom{-}e^{2} - 6$
71 $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{3} - \frac{5}{2}e^{2} + \frac{51}{2}e + 15$
79 $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ $\phantom{-}e^{4} - 3e^{3} - 8e^{2} + 15e + 14$
79 $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{5}{2}e^{2} + \frac{9}{2}e - 1$
81 $[81, 3, -3]$ $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 14e + 10$
83 $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ $\phantom{-}e^{4} - 4e^{3} - 8e^{2} + 26e + 24$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w^{3} - 3w^{2} - w + 2]$ $1$
$5$ $[5, 5, w^{2} - 2w - 3]$ $1$