Properties

Label 3.3.1772.1-10.1-a
Base field 3.3.1772.1
Weight $[2, 2, 2]$
Level norm $10$
Level $[10, 10, -\frac{1}{2}w^{2} + \frac{3}{2}w]$
Dimension $1$
CM no
Base change no

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Base field 3.3.1772.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x + 8\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[10, 10, -\frac{1}{2}w^{2} + \frac{3}{2}w]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ $-1$
2 $[2, 2, -w^{2} + 11]$ $\phantom{-}0$
3 $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ $-1$
5 $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ $-1$
9 $[9, 3, -\frac{1}{2}w^{2} + \frac{5}{2}w - 1]$ $-4$
25 $[25, 5, \frac{7}{2}w^{2} - \frac{31}{2}w + 9]$ $\phantom{-}1$
29 $[29, 29, -\frac{5}{2}w^{2} + \frac{1}{2}w + 29]$ $-6$
41 $[41, 41, -w^{2} + 3w - 1]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{2}w^{2} - \frac{3}{2}w + 3]$ $\phantom{-}6$
41 $[41, 41, 2w + 7]$ $\phantom{-}6$
43 $[43, 43, -\frac{7}{2}w^{2} - \frac{1}{2}w + 37]$ $-8$
43 $[43, 43, \frac{1}{2}w^{2} - \frac{9}{2}w + 3]$ $\phantom{-}8$
43 $[43, 43, \frac{1}{2}w^{2} - \frac{1}{2}w + 1]$ $\phantom{-}1$
47 $[47, 47, -w^{2} + w + 15]$ $-6$
53 $[53, 53, -2w^{2} + 2w + 29]$ $-6$
59 $[59, 59, w^{2} - w - 13]$ $\phantom{-}6$
67 $[67, 67, -\frac{1}{2}w^{2} + \frac{1}{2}w + 9]$ $\phantom{-}4$
71 $[71, 71, 2w - 3]$ $-9$
73 $[73, 73, \frac{3}{2}w^{2} - \frac{11}{2}w + 1]$ $-2$
79 $[79, 79, -\frac{3}{2}w^{2} + \frac{15}{2}w - 5]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ $1$
$5$ $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ $1$