# Properties

 Label 4.4.19525.1-19.1-d Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ Dimension $19$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.19525.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 14x^{2} + 15x + 45$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ Dimension: $19$ CM: no Base change: no Newspace dimension: $40$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{19} + 6x^{18} - 34x^{17} - 264x^{16} + 266x^{15} + 4364x^{14} + 2747x^{13} - 32557x^{12} - 52997x^{11} + 95163x^{10} + 275170x^{9} + 13222x^{8} - 477317x^{7} - 358851x^{6} + 183758x^{5} + 298401x^{4} + 64537x^{3} - 36518x^{2} - 12908x + 200$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}e$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $...$
9 $[9, 3, -w + 3]$ $...$
9 $[9, 3, w + 2]$ $...$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $...$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $...$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $...$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $...$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $...$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $...$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $...$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $...$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $...$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $...$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $...$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $...$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $-1$