Properties

 Label 4.4.19429.1-21.1-d Base field 4.4.19429.1 Weight $[2, 2, 2, 2]$ Level norm $21$ Level $[21, 21, w^{2} - w - 6]$ Dimension $2$ CM no Base change no

Related objects

• L-function not available

Learn more about

Base field 4.4.19429.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[21, 21, w^{2} - w - 6]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $37$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + x - 4$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $-1$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}4$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-2$
16 $[16, 2, 2]$ $\phantom{-}2e + 3$
17 $[17, 17, -w + 2]$ $\phantom{-}2$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-4$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-e - 4$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-2e - 2$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-3e$
41 $[41, 41, w^{2} - w - 1]$ $-2$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-5e - 2$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-e - 4$
53 $[53, 53, -w - 3]$ $\phantom{-}2e - 2$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}3e + 6$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-e$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $\phantom{-}e - 6$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $-5e - 2$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}2e + 8$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $1$
$7$ $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-1$