# Properties

 Label 4.4.19225.1-29.1-b Base field 4.4.19225.1 Weight $[2, 2, 2, 2]$ Level norm $29$ Level $[29, 29, w + 1]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[29, 29, w + 1]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $67$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 3x + 1$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}e + 2$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}4e + 5$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $-3$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-3e - 5$
11 $[11, 11, -w - 3]$ $-e - 3$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $\phantom{-}e + 2$
29 $[29, 29, w + 1]$ $\phantom{-}1$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}6e + 8$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}3$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-3$
31 $[31, 31, -w + 3]$ $\phantom{-}2e + 3$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-3$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}4e + 5$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}6e + 5$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $-5e - 13$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-13e - 19$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $-e + 6$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}5e + 6$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $-9e - 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w + 1]$ $-1$