# Properties

 Label 4.4.17600.1-19.4-b Base field 4.4.17600.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,-\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w + 5]$ Dimension $17$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17600.1

Generator $$w$$, with minimal polynomial $$x^{4} - 14x^{2} + 44$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19,19,-\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w + 5]$ Dimension: $17$ CM: no Base change: no Newspace dimension: $34$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{17} + 10x^{16} + 18x^{15} - 119x^{14} - 437x^{13} + 348x^{12} + 2943x^{11} + 718x^{10} - 9488x^{9} - 5967x^{8} + 16632x^{7} + 13026x^{6} - 16054x^{5} - 13131x^{4} + 7829x^{3} + 6138x^{2} - 1447x - 1031$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $...$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $...$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $...$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $...$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $...$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $...$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $\phantom{-}1$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $...$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $...$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $...$
31 $[31, 31, -w - 1]$ $...$
31 $[31, 31, w - 1]$ $...$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $...$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $...$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $...$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $...$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $...$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $...$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w + 5]$ $-1$