Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 9
Level $[9, 9, w^{2} - w - 2]$
Label 5.5.160801.1-9.3-d
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 $[9, 9, w^{2} - w - 2]$
Label 5.5.160801.1-9.3-d
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 3x^{3} \) \(\mathstrut -\mathstrut 22x^{2} \) \(\mathstrut +\mathstrut 61x \) \(\mathstrut +\mathstrut 43\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}0$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}e - 1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-\frac{1}{2}e^{3} - e^{2} + 9e + \frac{23}{2}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}e^{3} + e^{2} - 18e - 9$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $-\frac{1}{2}e^{3} + 9e + \frac{1}{2}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{1}{2}e^{3} + 9e - \frac{7}{2}$
31 $[31, 31, w^{3} - 4w + 2]$ $-e^{3} - e^{2} + 17e + 12$
32 $[32, 2, 2]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 10e - \frac{21}{2}$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}e^{3} + e^{2} - 18e - 8$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $\phantom{-}2e^{3} + 2e^{2} - 35e - 23$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}2e - 4$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $\phantom{-}e^{3} - 19e + 2$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}e^{3} - 18e + 5$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-e^{3} + 18e - 1$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $-4$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-2e^{3} - 3e^{2} + 35e + 39$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - 9e + \frac{19}{2}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-\frac{1}{2}e^{3} + 7e - \frac{11}{2}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-2e^{3} - 2e^{2} + 36e + 24$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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