# Properties

 Label 4.4.8789.1-29.2-b Base field 4.4.8789.1 Weight $[2, 2, 2, 2]$ Level norm $29$ Level $[29, 29, w^{2} - w - 3]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} - 2x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[29, 29, w^{2} - w - 3]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $20$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 5x^{3} + 2x^{2} - 18x - 19$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}e^{3} + 3e^{2} - 5e - 12$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}e^{2} + e - 3$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-e^{3} - 4e^{2} + 2e + 13$
16 $[16, 2, 2]$ $\phantom{-}e^{3} + 2e^{2} - 3e - 5$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}2e^{3} + 5e^{2} - 9e - 20$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-2e^{3} - 5e^{2} + 9e + 18$
17 $[17, 17, -w^{2} + 2w + 1]$ $-e^{3} - 4e^{2} + 3e + 14$
19 $[19, 19, w^{2} - w - 2]$ $-4e^{3} - 11e^{2} + 14e + 34$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}2e^{3} + 5e^{2} - 9e - 21$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}1$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-2e^{3} - 4e^{2} + 11e + 12$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $\phantom{-}5e^{3} + 14e^{2} - 21e - 53$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}e^{3} + 3e^{2} - 5e - 6$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}2e^{3} + 7e^{2} - 7e - 30$
61 $[61, 61, -w - 3]$ $\phantom{-}5e^{3} + 12e^{2} - 18e - 30$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-5e^{3} - 14e^{2} + 21e + 46$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}4e^{3} + 15e^{2} - 13e - 50$
81 $[81, 3, -3]$ $-6e^{3} - 19e^{2} + 20e + 64$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}4e^{2} + 4e - 19$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w^{2} - w - 3]$ $-1$