# Properties

 Label 4.4.10025.1-19.1-d Base field 4.4.10025.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.10025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 10x + 20$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $15$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 2x^{3} - 6x^{2} + 2x + 1$$
Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}2$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $-e^{3} + 2e^{2} + 7e - 2$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $-\frac{1}{2}e^{2} + e + \frac{5}{2}$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $-1$
19 $[19, 19, w - 1]$ $-3e^{3} + \frac{13}{2}e^{2} + 15e - \frac{9}{2}$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $-2e^{2} + 4e + 4$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{17}{2}e - 6$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $-3e^{3} + \frac{11}{2}e^{2} + 16e + \frac{5}{2}$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}2e^{3} - 5e^{2} - 10e + 9$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}3e^{3} - 6e^{2} - 15e + 2$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $-2e^{3} + 3e^{2} + 14e + 5$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $\phantom{-}2e^{3} - 4e^{2} - 12e + 4$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $\phantom{-}e^{3} - 2e^{2} - 7e - 6$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $\phantom{-}2e^{3} - 3e^{2} - 16e + 5$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $-\frac{3}{2}e^{3} + 4e^{2} + \frac{23}{2}e - 12$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $\phantom{-}\frac{5}{2}e^{3} - 7e^{2} - \frac{17}{2}e + 11$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $-e^{2} + 9$
81 $[81, 3, -3]$ $\phantom{-}4e^{3} - \frac{17}{2}e^{2} - 22e + \frac{9}{2}$
89 $[89, 89, w^{3} - 7w + 1]$ $\phantom{-}2e^{3} - 3e^{2} - 16e + 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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