# Properties

 Label 4.4.12725.1-1.1-b Base field 4.4.12725.1 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 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; 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: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + 4x^{2} - 10x - 24$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $-\frac{1}{2}e^{2} - e + 6$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}e$
11 $[11, 11, w - 2]$ $-\frac{1}{2}e^{2} - e + 6$
16 $[16, 2, 2]$ $\phantom{-}e + 5$
19 $[19, 19, w^{2} - 2w - 5]$ $\phantom{-}\frac{1}{2}e^{2} + e - 4$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}\frac{1}{2}e^{2} + e - 4$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}\frac{1}{2}e^{2} + e + 2$
29 $[29, 29, w]$ $-e - 3$
29 $[29, 29, 2w^{2} - w - 10]$ $-e - 3$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-e - 3$
29 $[29, 29, w - 1]$ $-e - 3$
31 $[31, 31, w^{3} - 6w - 6]$ $\phantom{-}2$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}2$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $-\frac{1}{2}e^{2} - 2e + 3$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $-\frac{1}{2}e^{2} - 2e + 3$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $-2e - 6$
59 $[59, 59, 2w^{2} - w - 13]$ $-2e - 6$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}\frac{1}{2}e^{2} + e - 7$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{1}{2}e^{2} + e - 7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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