Properties

Base field 4.4.2624.1
Weight [2, 2, 2, 2]
Level norm 47
Level $[47,47,-w^{2} + 3]$
Label 4.4.2624.1-47.2-a
Dimension 3
CM no
Base change no

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Base field 4.4.2624.1

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

Form

Weight [2, 2, 2, 2]
Level $[47,47,-w^{2} + 3]$
Label 4.4.2624.1-47.2-a
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 5x \) \(\mathstrut +\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $-\frac{1}{2}e^{2} + e + \frac{7}{2}$
7 $[7, 7, -w^{2} + w + 2]$ $-e^{2} + 5$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $\phantom{-}e^{2} - 2e - 5$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $-e^{2} + 2e + 5$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}e^{2} - 3$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $\phantom{-}2e^{2} - e - 5$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}e - 1$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $-\frac{1}{2}e^{2} - e + \frac{7}{2}$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $-1$
49 $[49, 7, w^{2} - 4w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{3}{2}$
71 $[71, 71, 2w - 3]$ $\phantom{-}\frac{5}{2}e^{2} - e - \frac{31}{2}$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}e^{2} - 4e - 1$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}\frac{9}{2}e^{2} - 5e - \frac{31}{2}$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $-e^{2} + 2e + 5$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $-\frac{5}{2}e^{2} + 3e + \frac{19}{2}$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-6e$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $\phantom{-}3e^{2} - 6e - 9$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $-e^{2} - 3e + 6$
81 $[81, 3, -3]$ $\phantom{-}3e^{2} - 17$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
47 $[47,47,-w^{2} + 3]$ $1$