# Properties

 Label 4.4.10025.1-1.1-a Base field 4.4.10025.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $4$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.10025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 10x + 20$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[1, 1, 1]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 2x^{3} - 8x^{2} - 12x + 5$$
Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{3}{2}$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{3}{2}$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $\phantom{-}e^{2} - 5$
19 $[19, 19, w - 1]$ $\phantom{-}e^{2} - 5$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $-e^{3} + 7e - 2$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $-e^{3} + 7e - 2$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e - \frac{5}{2}$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e - \frac{5}{2}$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}e^{3} - e^{2} - 9e + 5$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $\phantom{-}e^{3} - e^{2} - 9e + 5$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + \frac{13}{2}e + \frac{11}{2}$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + \frac{13}{2}e + \frac{11}{2}$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $-2e^{2} - 2e + 8$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $-2e^{2} - 2e + 8$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $\phantom{-}3e^{2} + 4e - 15$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $\phantom{-}3e^{2} + 4e - 15$
81 $[81, 3, -3]$ $-2e^{2} - 2e + 18$
89 $[89, 89, w^{3} - 7w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - \frac{9}{2}e - \frac{25}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.