# Properties

 Label 4.4.19525.1-19.2-c Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ 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: $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ 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 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $...$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}e$
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 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $...$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-1$
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
$19$ $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ $1$