Properties

 Label 4.4.4400.1-16.1-a Base field 4.4.4400.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change yes

Related objects

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Base field 4.4.4400.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} + 11$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 16x^{2} + 16$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}0$
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $\phantom{-}e$
11 $[11, 11, w]$ $-\frac{1}{2}e^{3} + 6e$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $-e^{2} + 10$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $-e^{2} + 10$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}0$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $\phantom{-}0$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $\phantom{-}\frac{1}{2}e^{3} - 9e$
41 $[41, 41, w^{3} - 5w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - 9e$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $-\frac{1}{2}e^{3} + 7e$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $-\frac{1}{2}e^{3} + 7e$
59 $[59, 59, -3w^{2} - w + 10]$ $\phantom{-}4$
59 $[59, 59, -3w^{2} + w + 10]$ $\phantom{-}4$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $\phantom{-}e^{3} - 15e$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $\phantom{-}e^{3} - 15e$
71 $[71, 71, 2w^{2} + w - 9]$ $-8$
71 $[71, 71, 2w^{2} - w - 9]$ $-8$
81 $[81, 3, -3]$ $\phantom{-}2$
101 $[101, 101, 2w^{2} - w - 10]$ $-e^{2} + 2$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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