# Properties

 Label 4.4.13025.1-4.2-a Base field 4.4.13025.1 Weight $[2, 2, 2, 2]$ Level norm $4$ Level $[4,2,w^{2} - w - 8]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 12x^{2} + 3x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[4,2,w^{2} - w - 8]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $2$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 2x - 4$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + w + 8]$ $-1$
5 $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $\phantom{-}\frac{3}{2}e - 1$
5 $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ $-e + 2$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $\phantom{-}e - 6$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ $-\frac{1}{2}e + 2$
29 $[29, 29, w]$ $\phantom{-}3e - 4$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ $-\frac{3}{2}e + 4$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ $\phantom{-}\frac{1}{2}e - 1$
29 $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ $-4$
41 $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ $-4e + 6$
41 $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ $\phantom{-}e$
61 $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ $-4e + 10$
61 $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ $\phantom{-}\frac{3}{2}e - 9$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ $\phantom{-}12$
79 $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ $-\frac{7}{2}e + 10$
81 $[81, 3, -3]$ $\phantom{-}\frac{9}{2}e - 8$
89 $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ $-\frac{11}{2}e + 8$
89 $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ $\phantom{-}\frac{11}{2}e + 1$
109 $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ $-\frac{7}{2}e + 13$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w^{2} - w - 8]$ $1$