# Properties

 Label 4.4.14272.1-1.1-a Base field 4.4.14272.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.14272.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 2x + 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[1, 1, 1]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} - 8x - 4$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $-2$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}e^{2} - 4$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}e^{2} - 2e - 8$
13 $[13, 13, -w + 2]$ $-e^{2} + 2e + 8$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $-e^{2} + e + 2$
19 $[19, 19, -w^{2} + w + 4]$ $-2e$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}2e^{2} - e - 8$
23 $[23, 23, w^{2} - 2w - 1]$ $-2e + 4$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $-e + 4$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $-e^{2} + 4$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $-e^{2} + 2e + 4$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $-e^{2} - e + 6$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $-e^{2} - 2e + 8$
59 $[59, 59, w - 4]$ $\phantom{-}2e - 4$
67 $[67, 67, 2w^{2} - 3w - 8]$ $-e^{2}$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $\phantom{-}e^{2} + e - 2$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $-e^{2} + 3e + 10$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $\phantom{-}e^{2} - 2$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $-e^{2} + 5e + 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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