Properties

Label 3.3.1304.1-6.1-c
Base field 3.3.1304.1
Weight $[2, 2, 2]$
Level norm $6$
Level $[6, 6, -w^{2} + 10]$
Dimension $1$
CM no
Base change no

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Base field 3.3.1304.1

Generator \(w\), with minimal polynomial \(x^{3} - 11x - 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[6, 6, -w^{2} + 10]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $-1$
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $-1$
3 $[3, 3, -w^{2} + 3w + 1]$ $-1$
9 $[9, 3, w^{2} + w - 7]$ $-2$
11 $[11, 11, 2w^{2} - 21]$ $-4$
17 $[17, 17, -\frac{1}{2}w^{2} + \frac{5}{2}w]$ $-2$
19 $[19, 19, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ $\phantom{-}0$
37 $[37, 37, w^{2} - w - 13]$ $-6$
37 $[37, 37, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $\phantom{-}6$
37 $[37, 37, \frac{5}{2}w^{2} - \frac{17}{2}w - 2]$ $\phantom{-}2$
47 $[47, 47, -\frac{3}{2}w^{2} + \frac{11}{2}w]$ $\phantom{-}8$
53 $[53, 53, w^{2} - w - 7]$ $\phantom{-}6$
59 $[59, 59, 2w - 1]$ $\phantom{-}12$
61 $[61, 61, -\frac{3}{2}w^{2} + \frac{3}{2}w + 20]$ $\phantom{-}2$
67 $[67, 67, w^{2} - 3w - 3]$ $\phantom{-}0$
71 $[71, 71, w^{2} - w - 1]$ $-8$
73 $[73, 73, 3w^{2} - w - 33]$ $-2$
79 $[79, 79, w^{2} - w - 11]$ $\phantom{-}8$
79 $[79, 79, w^{2} - 3w + 1]$ $-8$
79 $[79, 79, -2w - 5]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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