Properties

Label 4.4.13625.1-11.2-c
Base field 4.4.13625.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11,11,-\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$
Dimension $1$
CM no
Base change no

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Base field 4.4.13625.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11,11,-\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ $-1$
4 $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ $\phantom{-}3$
5 $[5, 5, w - 3]$ $-2$
11 $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ $-4$
11 $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ $-1$
19 $[19, 19, -w^{2} + 2w + 4]$ $\phantom{-}4$
19 $[19, 19, -w^{2} + 5]$ $\phantom{-}4$
31 $[31, 31, w]$ $\phantom{-}8$
31 $[31, 31, w + 3]$ $\phantom{-}0$
31 $[31, 31, -w + 4]$ $\phantom{-}8$
31 $[31, 31, w - 1]$ $\phantom{-}8$
41 $[41, 41, -w^{2} + 2]$ $\phantom{-}6$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ $-2$
59 $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ $-12$
59 $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ $\phantom{-}12$
79 $[79, 79, -w^{2} + 8]$ $\phantom{-}16$
79 $[79, 79, w^{2} - 2w - 7]$ $-8$
81 $[81, 3, -3]$ $\phantom{-}2$
101 $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ $-14$
101 $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11,11,-\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ $1$