# Properties

 Label 4.4.18625.1-20.1-f Base field 4.4.18625.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, w + 1]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18625.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 14x^{2} + 9x + 41$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, w + 1]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $32$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + x^{2} - 4x - 3$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}e$
4 $[4, 2, w - 3]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $-1$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $\phantom{-}e^{2} - 2e - 4$
9 $[9, 3, -w - 2]$ $\phantom{-}e^{2} + e - 4$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $\phantom{-}e^{2} + e - 5$
11 $[11, 11, -w + 2]$ $\phantom{-}e - 1$
41 $[41, 41, -w]$ $\phantom{-}2e^{2} - 3e - 12$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $-e + 1$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $\phantom{-}e^{2} + e - 5$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $\phantom{-}e^{2} + e + 1$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $\phantom{-}e^{2} - e - 5$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $-e^{2} - e + 1$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $-2e^{2} - 2e + 3$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $-3e^{2} - 4e + 8$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $\phantom{-}9$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $\phantom{-}2e^{2} + e - 14$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $-4e^{2} - 5e + 13$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $-4e^{2} + 3e + 20$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $\phantom{-}4e + 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w - 3]$ $-1$
$5$ $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $1$