# Properties

 Base field 6.6.1241125.1 Weight [2, 2, 2, 2, 2, 2] Level norm 49 Level $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ Label 6.6.1241125.1-49.1-a Dimension 15 CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.1241125.1

Generator $$w$$, with minimal polynomial $$x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2, 2, 2] Level $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ Label 6.6.1241125.1-49.1-a Dimension 15 Is CM no Is base change no Parent newspace dimension 37

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{15}$$ $$\mathstrut +\mathstrut 7x^{14}$$ $$\mathstrut -\mathstrut 22x^{13}$$ $$\mathstrut -\mathstrut 237x^{12}$$ $$\mathstrut +\mathstrut 9x^{11}$$ $$\mathstrut +\mathstrut 2807x^{10}$$ $$\mathstrut +\mathstrut 2194x^{9}$$ $$\mathstrut -\mathstrut 15492x^{8}$$ $$\mathstrut -\mathstrut 15198x^{7}$$ $$\mathstrut +\mathstrut 45065x^{6}$$ $$\mathstrut +\mathstrut 38286x^{5}$$ $$\mathstrut -\mathstrut 72076x^{4}$$ $$\mathstrut -\mathstrut 36653x^{3}$$ $$\mathstrut +\mathstrut 56862x^{2}$$ $$\mathstrut +\mathstrut 7630x$$ $$\mathstrut -\mathstrut 13354$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $\phantom{-}e$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $...$
11 $[11, 11, w - 1]$ $...$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $...$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $...$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $...$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $\phantom{-}1$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $...$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $...$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $...$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $...$
64 $[64, 2, 2]$ $...$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $...$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $...$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $...$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $...$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $...$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $...$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $...$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $-1$