# Properties

 Base field 3.3.321.1 Weight [2, 2, 2] Level norm 31 Level $[31, 31, 2w - 3]$ Label 3.3.321.1-31.1-b Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.321.1

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

## Form

 Weight [2, 2, 2] Level $[31, 31, 2w - 3]$ Label 3.3.321.1-31.1-b Dimension 5 Is CM no Is base change no Parent newspace dimension 7

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5} - x^{4} - 9x^{3} + 8x^{2} + 12x - 8$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{4}e^{3} - \frac{9}{4}e^{2} + e + 3$
7 $[7, 7, w^{2} - 2]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{9}{2}e^{2} + 3e - 6$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{7}{2}e^{2} + 3e + 2$
11 $[11, 11, -w^{2} + w + 1]$ $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{11}{4}e^{2} + \frac{3}{2}e - 3$
23 $[23, 23, -w - 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + 5$
29 $[29, 29, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + 4e + 6$
31 $[31, 31, 2w - 3]$ $\phantom{-}1$
41 $[41, 41, -2w^{2} + 3w + 6]$ $\phantom{-}\frac{5}{4}e^{4} + \frac{1}{4}e^{3} - \frac{39}{4}e^{2} - \frac{7}{2}e + 11$
43 $[43, 43, w^{2} - 3w + 3]$ $\phantom{-}e^{4} - 8e^{2} + e + 2$
47 $[47, 47, w^{2} + w - 4]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{9}{2}e^{2} - 4e - 2$
49 $[49, 7, 2w^{2} - 3w - 3]$ $\phantom{-}e^{3} + e^{2} - 7e - 2$
53 $[53, 53, w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{5}{4}e^{2} + 11e + 1$
59 $[59, 59, 2w^{2} - w - 5]$ $-\frac{3}{2}e^{4} + e^{3} + 11e^{2} - \frac{9}{2}e - 3$
59 $[59, 59, w^{2} - w - 7]$ $-\frac{3}{4}e^{4} + \frac{3}{4}e^{3} + \frac{19}{4}e^{2} - 2e + 1$
59 $[59, 59, -w^{2} - w + 7]$ $\phantom{-}\frac{5}{4}e^{4} + \frac{5}{4}e^{3} - \frac{47}{4}e^{2} - \frac{17}{2}e + 17$
67 $[67, 67, 2w^{2} - 3w - 7]$ $\phantom{-}e^{4} + e^{3} - 9e^{2} - 6e + 6$
73 $[73, 73, -w^{2} + 4w - 5]$ $\phantom{-}e^{4} - \frac{1}{2}e^{3} - \frac{17}{2}e^{2} + \frac{13}{2}e + 5$
79 $[79, 79, w^{2} - 8]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{7}{2}e^{2} - 6e$
79 $[79, 79, w^{2} - 5w + 5]$ $-2e^{4} - \frac{1}{2}e^{3} + \frac{39}{2}e^{2} + \frac{11}{2}e - 25$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, 2w - 3]$ $-1$