Properties

 Base field 4.4.2624.1 Weight [2, 2, 2, 2] Level norm 49 Level $[49, 7, 2w^{3} - 4w^{2} - 4w + 1]$ Label 4.4.2624.1-49.1-d Dimension 3 CM no Base change yes

Related objects

• L-function not available

Base field 4.4.2624.1

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

Form

 Weight [2, 2, 2, 2] Level $[49, 7, 2w^{3} - 4w^{2} - 4w + 1]$ Label 4.4.2624.1-49.1-d Dimension 3 Is CM no Is base change yes Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut 2x^{2}$$ $$\mathstrut -\mathstrut 9x$$ $$\mathstrut +\mathstrut 6$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $\phantom{-}1$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $\phantom{-}0$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $\phantom{-}0$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $-2e$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $-2e$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-2e^{2} + 2e + 10$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $-2e + 4$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $-2e + 4$
49 $[49, 7, w^{2} - 4w - 1]$ $\phantom{-}2e + 4$
71 $[71, 71, 2w - 3]$ $\phantom{-}2e^{2} - 4e - 12$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}2e^{2} - 4e - 12$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $-2e^{2} + 4e + 14$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $-2e^{2} + 4e + 14$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $\phantom{-}2e - 8$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}2e - 8$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $-2e$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $-2e$
81 $[81, 3, -3]$ $-2e^{2} + 2e + 14$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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