# Properties

 Label 4.4.15125.1-19.2-h Base field 4.4.15125.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,-w^{3} - w^{2} + 9w + 3]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.15125.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 14x^{2} + 14x + 31$$; narrow class number $$4$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19,19,-w^{3} - w^{2} + 9w + 3]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $24$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 28x^{4} + 207x^{2} - 162$$
Norm Prime Eigenvalue
5 $[5, 5, 4w^{3} + 7w^{2} - 37w - 45]$ $\phantom{-}e$
11 $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ $-\frac{1}{27}e^{5} + \frac{19}{27}e^{3} - \frac{10}{3}e$
11 $[11, 11, -w + 2]$ $\phantom{-}\frac{2}{27}e^{5} - \frac{29}{27}e^{3} + \frac{1}{3}e$
16 $[16, 2, 2]$ $-\frac{1}{9}e^{4} + \frac{10}{9}e^{2} + 1$
19 $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ $-\frac{4}{9}e^{4} + \frac{58}{9}e^{2} - 4$
19 $[19, 19, -w^{3} - w^{2} + 9w + 3]$ $-1$
19 $[19, 19, -2w^{3} - 4w^{2} + 17w + 23]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{13}{3}e$
19 $[19, 19, w^{3} + 2w^{2} - 10w - 10]$ $\phantom{-}\frac{1}{27}e^{5} - \frac{19}{27}e^{3} + \frac{10}{3}e$
29 $[29, 29, -w - 2]$ $\phantom{-}\frac{1}{9}e^{4} - \frac{19}{9}e^{2} + 12$
29 $[29, 29, -w^{3} - 2w^{2} + 8w + 15]$ $\phantom{-}\frac{5}{9}e^{4} - \frac{77}{9}e^{2} + 14$
29 $[29, 29, 2w^{3} + 3w^{2} - 18w - 20]$ $-\frac{1}{27}e^{5} + \frac{10}{27}e^{3} + 3e$
29 $[29, 29, -3w^{3} - 5w^{2} + 27w + 28]$ $\phantom{-}\frac{2}{9}e^{5} - \frac{35}{9}e^{3} + \frac{35}{3}e$
31 $[31, 31, 3w^{3} + 5w^{2} - 27w - 31]$ $\phantom{-}\frac{1}{9}e^{5} - \frac{13}{9}e^{3} - \frac{5}{3}e$
31 $[31, 31, -3w^{3} - 5w^{2} + 27w + 30]$ $-\frac{2}{27}e^{5} + \frac{29}{27}e^{3} - \frac{4}{3}e$
31 $[31, 31, -2w^{3} - 3w^{2} + 18w + 17]$ $-\frac{2}{27}e^{5} + \frac{20}{27}e^{3} + 5e$
31 $[31, 31, 2w^{3} + 3w^{2} - 18w - 18]$ $\phantom{-}\frac{5}{27}e^{5} - \frac{95}{27}e^{3} + \frac{41}{3}e$
71 $[71, 71, -w^{3} - 2w^{2} + 10w + 8]$ $-\frac{2}{3}e^{4} + \frac{29}{3}e^{2} - 2$
71 $[71, 71, 4w^{3} + 8w^{2} - 35w - 50]$ $\phantom{-}\frac{11}{9}e^{4} - \frac{164}{9}e^{2} + 22$
71 $[71, 71, -4w^{3} - 7w^{2} + 36w + 47]$ $-\frac{8}{9}e^{4} + \frac{125}{9}e^{2} - 22$
71 $[71, 71, -w^{3} - 2w^{2} + 8w + 17]$ $-\frac{2}{9}e^{4} + \frac{11}{9}e^{2} + 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-w^{3} - w^{2} + 9w + 3]$ $1$