Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 9
Level $[9, 3, -w^{4} + 5w^{2} - 3]$
Label 5.5.160801.1-9.1-f
Dimension 4
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 $[9, 3, -w^{4} + 5w^{2} - 3]$
Label 5.5.160801.1-9.1-f
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 20x^{2} \) \(\mathstrut -\mathstrut 21x \) \(\mathstrut -\mathstrut 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - \frac{41}{3}e - \frac{23}{3}$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-1$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}e$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{4}{3}e^{3} - \frac{2}{3}e^{2} - \frac{76}{3}e - \frac{43}{3}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{19}{3}e - \frac{1}{3}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{16}{3}e - \frac{5}{3}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{4}{3}e^{3} + \frac{2}{3}e^{2} + \frac{76}{3}e + \frac{37}{3}$
31 $[31, 31, w^{3} - 4w + 2]$ $-e^{3} + e^{2} + 20e + 7$
32 $[32, 2, 2]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - \frac{38}{3}e - \frac{41}{3}$
37 $[37, 37, w^{3} - 3w - 1]$ $-2e^{3} + e^{2} + 37e + 23$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{44}{3}e + \frac{2}{3}$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-\frac{7}{3}e^{3} + \frac{2}{3}e^{2} + \frac{139}{3}e + \frac{70}{3}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-\frac{5}{3}e^{3} + \frac{4}{3}e^{2} + \frac{95}{3}e + \frac{41}{3}$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{19}{3}e + \frac{19}{3}$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $\phantom{-}\frac{5}{3}e^{3} - \frac{4}{3}e^{2} - \frac{92}{3}e - \frac{44}{3}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}\frac{7}{3}e^{3} - \frac{5}{3}e^{2} - \frac{139}{3}e - \frac{55}{3}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{22}{3}e - \frac{43}{3}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{2}{3}e^{3} + \frac{4}{3}e^{2} + \frac{32}{3}e - \frac{13}{3}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-\frac{8}{3}e^{3} + \frac{7}{3}e^{2} + \frac{152}{3}e + \frac{62}{3}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-2e^{3} + e^{2} + 38e + 29$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $1$