Properties

Label 5.5.157457.1-25.1-d
Base field 5.5.157457.1
Weight $[2, 2, 2, 2, 2]$
Level norm $25$
Level $[25, 25, -w^{3} + w^{2} + 3w - 2]$
Dimension $5$
CM no
Base change no

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Base field 5.5.157457.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[25, 25, -w^{3} + w^{2} + 3w - 2]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} + x^{4} - 12x^{3} - 9x^{2} + 20x + 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}e$
5 $[5, 5, w^{2} - w - 2]$ $\phantom{-}0$
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ $\phantom{-}\frac{1}{3}e^{4} - 4e^{2} + \frac{17}{3}$
13 $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{1}{6}e^{4} - \frac{1}{2}e^{3} + 2e^{2} + \frac{7}{2}e - \frac{13}{3}$
29 $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ $-\frac{1}{3}e^{4} + 4e^{2} - \frac{26}{3}$
29 $[29, 29, -w^{2} + 2w + 3]$ $-\frac{1}{3}e^{4} + 3e^{2} - 2e - \frac{2}{3}$
31 $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $\phantom{-}\frac{1}{6}e^{4} - \frac{1}{2}e^{3} - 3e^{2} + \frac{9}{2}e + \frac{19}{3}$
31 $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 6e^{2} + \frac{11}{2}e - 9$
32 $[32, 2, 2]$ $\phantom{-}\frac{5}{6}e^{4} + \frac{1}{2}e^{3} - 10e^{2} - \frac{7}{2}e + \frac{29}{3}$
43 $[43, 43, -w^{2} - w + 4]$ $-\frac{1}{3}e^{4} - e^{3} + 4e^{2} + 10e - \frac{17}{3}$
53 $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ $\phantom{-}e^{2} - 3e - 7$
53 $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ $\phantom{-}e^{4} + e^{3} - 10e^{2} - 8e + 8$
73 $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ $\phantom{-}e^{3} + e^{2} - 8e - 8$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-\frac{2}{3}e^{4} - e^{3} + 6e^{2} + 6e - \frac{4}{3}$
81 $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ $\phantom{-}e^{3} + e^{2} - 11e - 4$
83 $[83, 83, w^{3} - w^{2} - 5w]$ $\phantom{-}\frac{2}{3}e^{4} + e^{3} - 7e^{2} - 5e + \frac{10}{3}$
89 $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ $-\frac{1}{3}e^{4} + 3e^{2} - 2e - \frac{20}{3}$
97 $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $\phantom{-}e^{4} + e^{3} - 11e^{2} - 5e + 12$
101 $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ $-3e$
103 $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ $-e^{2} - 3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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