# Properties

 Label 4.4.19025.1-1.1-a Base field 4.4.19025.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $3$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.19025.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 13x^{2} + 14x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[1, 1, 1]$ Dimension: $3$ CM: no Base change: yes Newspace dimension: $7$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} - x^{2} - 9x + 5$$
Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{7}{2}$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{7}{2}$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $\phantom{-}0$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $\phantom{-}0$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $\phantom{-}e^{2} - 5$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $\phantom{-}e^{2} - 5$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $-\frac{1}{2}e^{2} + e - \frac{5}{2}$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $-e^{2} - e + 10$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $-e^{2} - e + 10$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $-\frac{1}{2}e^{2} + e - \frac{5}{2}$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $\phantom{-}e^{2} - 3e - 2$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $\phantom{-}e^{2} - 3e - 2$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $\phantom{-}e^{2} - 2e - 7$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $\phantom{-}e^{2} - 2e - 7$
81 $[81, 3, -3]$ $\phantom{-}10$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $-\frac{5}{2}e^{2} - e + \frac{35}{2}$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $-e^{2} - e + 10$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $-e^{2} - e + 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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