Properties

Label 3.3.404.1-33.1-a
Base field 3.3.404.1
Weight $[2, 2, 2]$
Level norm $33$
Level $[33, 33, 2w - 5]$
Dimension $1$
CM no
Base change no

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Base field 3.3.404.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[33, 33, 2w - 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $-1$
3 $[3, 3, w^{2} - 2w - 2]$ $\phantom{-}1$
7 $[7, 7, -w + 2]$ $-2$
9 $[9, 3, w^{2} - 2]$ $-2$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}1$
29 $[29, 29, -2w + 1]$ $-10$
37 $[37, 37, 2w^{2} - 4w - 3]$ $\phantom{-}6$
37 $[37, 37, -w^{2} + 3w + 3]$ $-10$
37 $[37, 37, 2w^{2} - w - 8]$ $-4$
41 $[41, 41, w^{2} - 4w + 2]$ $-10$
43 $[43, 43, -2w^{2} + 2w + 7]$ $-8$
43 $[43, 43, -2w^{2} + 3w + 6]$ $\phantom{-}0$
43 $[43, 43, -w^{2} + 6]$ $-2$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}2$
53 $[53, 53, 2w^{2} - 5w - 4]$ $\phantom{-}4$
59 $[59, 59, 2w - 3]$ $-14$
61 $[61, 61, -w - 4]$ $\phantom{-}4$
67 $[67, 67, -2w^{2} - w + 2]$ $\phantom{-}2$
73 $[73, 73, 2w^{2} - 3w - 12]$ $\phantom{-}6$
83 $[83, 83, -2w - 5]$ $\phantom{-}12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w^{2} - 2w - 2]$ $-1$
$11$ $[11, 11, -w^{2} + 2w + 4]$ $-1$