# Properties

 Label 3.3.316.1-19.1-b Base field 3.3.316.1 Weight $[2, 2, 2]$ Level norm $19$ Level $[19, 19, w^{2} - w + 1]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.316.1

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

## Form

 Weight: $[2, 2, 2]$ Level: $[19, 19, w^{2} - w + 1]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $7$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - x^{5} - 12x^{4} + 12x^{3} + 35x^{2} - 31x - 12$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $-\frac{1}{4}e^{5} + \frac{5}{2}e^{3} - \frac{21}{4}e$
11 $[11, 11, w^{2} - w - 1]$ $-\frac{1}{4}e^{5} - \frac{1}{2}e^{4} + \frac{5}{2}e^{3} + \frac{7}{2}e^{2} - \frac{25}{4}e - 3$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{5}{2}e^{3} - \frac{9}{2}e^{2} + \frac{21}{4}e + 9$
19 $[19, 19, w^{2} - w + 1]$ $\phantom{-}1$
23 $[23, 23, 2w - 3]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{9}{2}e^{2} - \frac{7}{4}e + 9$
27 $[27, 3, 3]$ $\phantom{-}2e - 2$
29 $[29, 29, 2w + 1]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{5}{2}e^{3} + \frac{9}{2}e^{2} + \frac{21}{4}e - 3$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}\frac{3}{4}e^{5} + \frac{1}{2}e^{4} - \frac{17}{2}e^{3} - \frac{5}{2}e^{2} + \frac{83}{4}e - 1$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-2e^{2} + 8$
41 $[41, 41, 2w^{2} - 9]$ $-\frac{1}{4}e^{5} + \frac{1}{2}e^{4} + \frac{3}{2}e^{3} - \frac{11}{2}e^{2} + \frac{3}{4}e + 9$
43 $[43, 43, w^{2} + w - 5]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{21}{2}e + 2$
43 $[43, 43, -3w^{2} + w + 15]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 8$
43 $[43, 43, -2w^{2} + 2w + 11]$ $\phantom{-}e^{3} + 2e^{2} - 5e - 10$
53 $[53, 53, w^{2} - w - 7]$ $-e^{5} + 11e^{3} - 26e + 6$
61 $[61, 61, 4w^{2} - 2w - 15]$ $-\frac{3}{4}e^{5} - \frac{1}{2}e^{4} + \frac{13}{2}e^{3} + \frac{7}{2}e^{2} - \frac{39}{4}e - 1$
67 $[67, 67, -5w^{2} + 3w + 23]$ $-\frac{3}{4}e^{5} - \frac{3}{2}e^{4} + \frac{15}{2}e^{3} + \frac{21}{2}e^{2} - \frac{67}{4}e - 7$
73 $[73, 73, 2w^{2} - 3]$ $\phantom{-}\frac{1}{2}e^{5} - e^{4} - 6e^{3} + 7e^{2} + \frac{27}{2}e - 4$
73 $[73, 73, -3w^{2} - w + 7]$ $-\frac{1}{2}e^{5} + 5e^{3} - 2e^{2} - \frac{17}{2}e + 8$
73 $[73, 73, -6w^{2} + 4w + 25]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{5}{2}e^{3} + \frac{7}{2}e^{2} + \frac{9}{4}e - 1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, w^{2} - w + 1]$ $-1$