Properties

Label 4.4.5225.1-11.1-a
Base field 4.4.5225.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, w]$
Dimension $1$
CM no
Base change no

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Base field 4.4.5225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, w]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 3w - \frac{7}{2}]$ $\phantom{-}1$
4 $[4, 2, w + 1]$ $\phantom{-}3$
11 $[11, 11, w]$ $-1$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{5}{2}]$ $\phantom{-}4$
11 $[11, 11, -w + 2]$ $\phantom{-}0$
19 $[19, 19, -\frac{1}{2}w^{3} + 3w + \frac{3}{2}]$ $\phantom{-}0$
25 $[25, 5, -w^{3} + 2w^{2} + 4w - 4]$ $-2$
31 $[31, 31, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}0$
31 $[31, 31, -\frac{1}{2}w^{3} + w^{2} + w - \frac{1}{2}]$ $-4$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{15}{2}]$ $\phantom{-}4$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w - \frac{5}{2}]$ $\phantom{-}0$
61 $[61, 61, -2w^{3} + 5w^{2} + 8w - 12]$ $-10$
61 $[61, 61, \frac{1}{2}w^{3} - 2w - \frac{5}{2}]$ $-6$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} - \frac{15}{2}]$ $-4$
71 $[71, 71, \frac{3}{2}w^{3} - 4w^{2} - 5w + \frac{23}{2}]$ $-16$
79 $[79, 79, -\frac{5}{2}w^{3} + 6w^{2} + 9w - \frac{31}{2}]$ $-8$
79 $[79, 79, -4w^{3} + 10w^{2} + 17w - 28]$ $\phantom{-}12$
79 $[79, 79, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}0$
79 $[79, 79, \frac{5}{2}w^{3} - 6w^{2} - 9w + \frac{23}{2}]$ $\phantom{-}8$
81 $[81, 3, -3]$ $-14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w]$ $1$