# Properties

 Base field 4.4.19225.1 Weight [2, 2, 2, 2] Level norm 9 Level $[9,3,-\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{19}{2}w - 28]$ Label 4.4.19225.1-9.2-d Dimension 3 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[9,3,-\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{19}{2}w - 28]$ Label 4.4.19225.1-9.2-d Dimension 3 Is CM no Is base change no Parent newspace dimension 17

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} - 9x - 1$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - \frac{11}{3}$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $-\frac{2}{3}e^{2} + \frac{1}{3}e + \frac{7}{3}$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}1$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-\frac{2}{3}e^{2} + \frac{4}{3}e + \frac{10}{3}$
11 $[11, 11, -w - 3]$ $-\frac{1}{3}e^{2} - \frac{1}{3}e - \frac{1}{3}$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-\frac{2}{3}e^{2} - \frac{2}{3}e + \frac{1}{3}$
29 $[29, 29, w + 1]$ $-e^{2} - 2e + 9$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $-\frac{1}{3}e^{2} + \frac{2}{3}e - \frac{13}{3}$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}e^{2} + e - 4$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $\phantom{-}e^{2} - 2e - 9$
31 $[31, 31, -w + 3]$ $\phantom{-}\frac{4}{3}e^{2} - \frac{2}{3}e - \frac{20}{3}$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{4}{3}e - \frac{8}{3}$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}e + 8$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}2e^{2} - 5$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e + \frac{4}{3}$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-3e - 1$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - \frac{8}{3}$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $-\frac{1}{3}e^{2} + \frac{11}{3}e + \frac{14}{3}$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{8}{3}e - \frac{34}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9,3,-\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{19}{2}w - 28]$ $-1$