Properties

Base field 4.4.2624.1
Weight [2, 2, 2, 2]
Level norm 73
Level $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$
Label 4.4.2624.1-73.1-c
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 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$
Label 4.4.2624.1-73.1-c
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut +\mathstrut 4x^{2} \) \(\mathstrut +\mathstrut x \) \(\mathstrut -\mathstrut 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $-e^{2} - e + 2$
7 $[7, 7, -w^{2} + w + 2]$ $-e - 2$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $\phantom{-}e - 2$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $-2e^{2} - 7e + 1$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}3e^{2} + 6e - 7$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $\phantom{-}3e^{2} + 6e - 7$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-2e^{2} - 3e - 1$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $\phantom{-}e^{2} - 2e - 9$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $-9$
49 $[49, 7, w^{2} - 4w - 1]$ $-2e^{2} - e + 6$
71 $[71, 71, 2w - 3]$ $-7e - 7$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}4e^{2} + 13e$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}1$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $-e^{2} - e - 4$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $-e^{2} - 3e - 3$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-2e^{2} - 4e + 3$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $\phantom{-}e^{2} + 6e + 1$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $\phantom{-}3e^{2} + 2e - 20$
81 $[81, 3, -3]$ $\phantom{-}e^{2} - 2e - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $-1$