# Properties

 Label 4.4.15125.1-19.3-f Base field 4.4.15125.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,-2w^{3} - 4w^{2} + 17w + 23]$ Dimension $4$ 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: $[19,19,-2w^{3} - 4w^{2} + 17w + 23]$ Dimension: $4$ 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:

 $$x^{4} - 10x^{2} + 8$$
Norm Prime Eigenvalue
5 $[5, 5, 4w^{3} + 7w^{2} - 37w - 45]$ $\phantom{-}0$
11 $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ $\phantom{-}\frac{1}{2}e^{3} - 3e$
11 $[11, 11, -w + 2]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-e^{2} + 7$
19 $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ $\phantom{-}\frac{1}{2}e^{3} - 4e$
19 $[19, 19, -w^{3} - w^{2} + 9w + 3]$ $\phantom{-}2e$
19 $[19, 19, -2w^{3} - 4w^{2} + 17w + 23]$ $-1$
19 $[19, 19, w^{3} + 2w^{2} - 10w - 10]$ $-e^{2} + 8$
29 $[29, 29, -w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 4e$
29 $[29, 29, -w^{3} - 2w^{2} + 8w + 15]$ $-\frac{1}{2}e^{3} + 8e$
29 $[29, 29, 2w^{3} + 3w^{2} - 18w - 20]$ $\phantom{-}e^{2}$
29 $[29, 29, -3w^{3} - 5w^{2} + 27w + 28]$ $-e^{2} + 8$
31 $[31, 31, 3w^{3} + 5w^{2} - 27w - 31]$ $\phantom{-}e^{3} - 9e$
31 $[31, 31, -3w^{3} - 5w^{2} + 27w + 30]$ $\phantom{-}\frac{1}{2}e^{3} - 5e$
31 $[31, 31, -2w^{3} - 3w^{2} + 18w + 17]$ $-\frac{3}{2}e^{3} + 13e$
31 $[31, 31, 2w^{3} + 3w^{2} - 18w - 18]$ $-\frac{1}{2}e^{3} + 7e$
71 $[71, 71, -w^{3} - 2w^{2} + 10w + 8]$ $\phantom{-}e^{2} - 4$
71 $[71, 71, 4w^{3} + 8w^{2} - 35w - 50]$ $-8$
71 $[71, 71, -4w^{3} - 7w^{2} + 36w + 47]$ $\phantom{-}e^{2} - 4$
71 $[71, 71, -w^{3} - 2w^{2} + 8w + 17]$ $-e^{2} + 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-2w^{3} - 4w^{2} + 17w + 23]$ $1$