# Properties

 Label 4.4.13025.1-16.3-b Base field 4.4.13025.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16,4,w + 1]$ Dimension $4$ 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: $[16,4,w + 1]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + x^{3} - 4x^{2} - 4x + 1$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + w + 8]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $-e - 1$
5 $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ $\phantom{-}e^{3} - 4e - 1$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $-4e^{3} + 13e + 1$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ $-e^{3} + 2e^{2} + e - 3$
29 $[29, 29, w]$ $-e^{3} + 2e^{2} + 2e - 9$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ $-e^{3} - e^{2} + e + 1$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ $\phantom{-}3e - 1$
29 $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ $\phantom{-}5e^{3} - 3e^{2} - 14e + 8$
41 $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ $-4e^{2} - e + 12$
41 $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ $\phantom{-}e^{3} + 3e^{2} - 3e - 5$
61 $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ $-2e^{3} + e^{2} + 10e - 3$
61 $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ $\phantom{-}6e^{3} - 6e^{2} - 17e + 12$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ $-5e^{3} + 6e^{2} + 18e - 12$
79 $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ $\phantom{-}4e^{3} - 8e - 2$
81 $[81, 3, -3]$ $\phantom{-}4e^{3} - 15e - 5$
89 $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ $\phantom{-}e^{3} + e^{2} - 3e + 1$
89 $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ $-4e^{3} - 2e^{2} + 14e + 6$
109 $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ $-e^{3} + 3e^{2} + 6e - 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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