# Properties

 Label 4.4.19525.1-1.1-a Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $2$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.19525.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 14x^{2} + 15x + 45$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[1, 1, 1]$ Dimension: $2$ CM: no Base change: yes Newspace dimension: $8$

## 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
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}e$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}e$
9 $[9, 3, -w + 3]$ $-e + 4$
9 $[9, 3, w + 2]$ $-e + 4$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $-4e + 8$
16 $[16, 2, 2]$ $\phantom{-}4e - 3$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}2e - 8$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $\phantom{-}2e - 8$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $-3e + 7$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-3e + 7$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $-2e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $-2e$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $-e - 1$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $-e - 1$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $-8e + 12$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $-8e + 12$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $\phantom{-}5e - 7$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $\phantom{-}8e - 14$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $\phantom{-}8e - 14$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $\phantom{-}5e - 7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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