# Properties

 Label 6.6.371293.1-53.5-c Base field $$\Q(\zeta_{13})^+$$ Weight $[2, 2, 2, 2, 2, 2]$ Level norm $53$ Level $[53,53,-w^{5} + 5w^{3} + w^{2} - 5w]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\zeta_{13})^+$$

Generator $$w$$, with minimal polynomial $$x^{6} - x^{5} - 5x^{4} + 4x^{3} + 6x^{2} - 3x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[53,53,-w^{5} + 5w^{3} + w^{2} - 5w]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} - 5x^{2} - 11x + 42$$
Norm Prime Eigenvalue
13 $[13, 13, w^{5} - 5w^{3} + 4w]$ $\phantom{-}e$
25 $[25, 5, w^{5} - 5w^{3} + 6w - 1]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{4}{3}e - 8$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}e - 5$
25 $[25, 5, w^{5} - 4w^{3} - w^{2} + 3w + 2]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - 3$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $-e + 2$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 3]$ $\phantom{-}\frac{2}{3}e^{2} - \frac{8}{3}e - 6$
53 $[53, 53, -w^{4} + w^{3} + 3w^{2} - 2w + 1]$ $-2e + 4$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $-\frac{2}{3}e^{2} + \frac{8}{3}e + 10$
53 $[53, 53, -w^{5} + w^{4} + 4w^{3} - 4w^{2} - 3w + 1]$ $-\frac{1}{3}e^{2} + \frac{1}{3}e + 7$
53 $[53, 53, w^{3} - 2w - 2]$ $\phantom{-}e^{2} - 3e - 9$
53 $[53, 53, w^{5} - 5w^{3} - w^{2} + 5w]$ $-1$
53 $[53, 53, -w^{4} + 4w^{2} + w - 4]$ $-\frac{2}{3}e^{2} - \frac{1}{3}e + 12$
64 $[64, 2, -2]$ $\phantom{-}2e - 1$
79 $[79, 79, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 9w + 2]$ $-\frac{4}{3}e^{2} + \frac{7}{3}e + 15$
79 $[79, 79, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 6w - 1]$ $-\frac{1}{3}e^{2} + \frac{7}{3}e + 7$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{1}{3}e - 11$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 9w + 3]$ $-e^{2} + e + 17$
79 $[79, 79, -2w^{4} + w^{3} + 7w^{2} - 3w - 3]$ $\phantom{-}\frac{4}{3}e^{2} - \frac{10}{3}e - 12$
79 $[79, 79, -w^{5} + 6w^{3} - w^{2} - 8w + 1]$ $\phantom{-}4$
103 $[103, 103, 2w^{4} - 7w^{2} - w + 3]$ $-\frac{2}{3}e^{2} - \frac{1}{3}e + 22$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,-w^{5} + 5w^{3} + w^{2} - 5w]$ $1$