Properties

 Label 4.4.12725.1-11.2-f Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $11$ Level $[11, 11, w^{2} - 5]$ Dimension $4$ CM no Base change no

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Base field 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[11, 11, w^{2} - 5]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} - 5x^{3} - 36x^{2} + 119x + 353$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{2} - 5]$ $-1$
11 $[11, 11, -w^{2} + 2w + 4]$ $-\frac{1}{9}e^{3} - \frac{2}{9}e^{2} + \frac{31}{9}e + \frac{116}{9}$
11 $[11, 11, w - 2]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{1}{9}e^{2} - \frac{31}{9}e - \frac{14}{9}$
16 $[16, 2, 2]$ $-\frac{1}{9}e^{3} - \frac{2}{9}e^{2} + \frac{40}{9}e + \frac{62}{9}$
19 $[19, 19, w^{2} - 2w - 5]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{1}{9}e^{2} - \frac{31}{9}e - \frac{32}{9}$
19 $[19, 19, -w^{2} + 6]$ $-\frac{1}{3}e^{2} + e + \frac{31}{3}$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}\frac{1}{9}e^{3} + \frac{2}{9}e^{2} - \frac{31}{9}e - \frac{89}{9}$
29 $[29, 29, w]$ $\phantom{-}\frac{1}{9}e^{3} + \frac{2}{9}e^{2} - \frac{31}{9}e - \frac{53}{9}$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}\frac{1}{3}e^{2} - e - \frac{31}{3}$
29 $[29, 29, -2w^{2} + 3w + 9]$ $\phantom{-}\frac{1}{9}e^{3} + \frac{2}{9}e^{2} - \frac{31}{9}e - \frac{53}{9}$
29 $[29, 29, w - 1]$ $-\frac{2}{9}e^{3} + \frac{5}{9}e^{2} + \frac{44}{9}e - \frac{20}{9}$
31 $[31, 31, w^{3} - 6w - 6]$ $-\frac{2}{9}e^{3} + \frac{5}{9}e^{2} + \frac{44}{9}e - \frac{11}{9}$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $-e + 3$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $\phantom{-}2$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $\phantom{-}\frac{1}{9}e^{3} + \frac{2}{9}e^{2} - \frac{40}{9}e - \frac{107}{9}$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{4}{9}e^{2} - \frac{4}{9}e + \frac{43}{9}$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{31}{3}e - 12$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $-\frac{2}{9}e^{3} + \frac{2}{9}e^{2} + \frac{44}{9}e + \frac{64}{9}$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-e - 1$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w^{2} - 5]$ $1$