Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 13
Level $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$
Label 5.5.160801.1-13.1-b
Dimension 2
CM no
Base change no

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Base field 5.5.160801.1

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

Form

Weight [2, 2, 2, 2, 2]
Level $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$
Label 5.5.160801.1-13.1-b
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut -\mathstrut 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-1$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-3$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}e$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-1$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $-1$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{2}{3}e - \frac{1}{3}$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}\frac{1}{3}e + \frac{7}{3}$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}\frac{5}{3}e - \frac{13}{3}$
32 $[32, 2, 2]$ $-\frac{4}{3}e + \frac{17}{3}$
37 $[37, 37, w^{3} - 3w - 1]$ $-\frac{4}{3}e - \frac{13}{3}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-\frac{4}{3}e - \frac{1}{3}$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-\frac{10}{3}e + \frac{11}{3}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $\phantom{-}\frac{4}{3}e - \frac{14}{3}$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{4}{3}e + \frac{13}{3}$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-3e + 4$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}3e - 6$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-\frac{2}{3}e + \frac{19}{3}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{4}{3}e - \frac{34}{3}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{3}e + \frac{25}{3}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $\phantom{-}\frac{5}{3}e + \frac{11}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $1$