Properties

Label 3.3.473.1-33.1-b
Base field 3.3.473.1
Weight $[2, 2, 2]$
Level norm $33$
Level $[33, 33, -w^{2} + 2w + 3]$
Dimension $2$
CM no
Base change no

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Base field 3.3.473.1

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

Form

Weight: $[2, 2, 2]$
Level: $[33, 33, -w^{2} + 2w + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-\frac{1}{2}e + 3$
9 $[9, 3, -w^{2} + w + 4]$ $\phantom{-}2$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}2$
11 $[11, 11, -w^{2} - w + 1]$ $-1$
13 $[13, 13, w + 3]$ $-e$
17 $[17, 17, -w^{2} + 2]$ $\phantom{-}e + 2$
25 $[25, 5, w^{2} + w - 4]$ $-e + 2$
37 $[37, 37, w^{2} + w - 5]$ $-e - 8$
41 $[41, 41, 2w^{2} + w - 6]$ $-2e + 2$
43 $[43, 43, w^{2} - 3w - 2]$ $-3e + 4$
43 $[43, 43, -w + 4]$ $\phantom{-}e - 4$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}3e - 4$
73 $[73, 73, 3w + 5]$ $-e + 2$
73 $[73, 73, w^{2} - 2w - 5]$ $\phantom{-}3e$
73 $[73, 73, w^{2} - 2w - 7]$ $\phantom{-}2e - 10$
79 $[79, 79, 2w^{2} + w - 9]$ $\phantom{-}e - 12$
83 $[83, 83, 3w^{2} - 2w - 13]$ $\phantom{-}5e$
89 $[89, 89, -w^{2} - 2w + 9]$ $\phantom{-}6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $-1$
$11$ $[11, 11, -w^{2} - w + 1]$ $1$