# Properties

 Base field 3.3.321.1 Weight [2, 2, 2] Level norm 23 Level $[23, 23, -w - 3]$ Label 3.3.321.1-23.1-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 $[23, 23, -w - 3]$ Label 3.3.321.1-23.1-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:
$$x^{5} - 3x^{4} - 9x^{3} + 26x^{2} + 10x - 37$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-\frac{3}{4}e^{4} + e^{3} + \frac{31}{4}e^{2} - \frac{21}{4}e - \frac{49}{4}$
7 $[7, 7, w^{2} - 2]$ $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} + \frac{1}{4}e - \frac{23}{4}$
8 $[8, 2, 2]$ $\phantom{-}\frac{7}{4}e^{4} - 2e^{3} - \frac{79}{4}e^{2} + \frac{41}{4}e + \frac{153}{4}$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}\frac{3}{2}e^{4} - 2e^{3} - \frac{33}{2}e^{2} + \frac{19}{2}e + \frac{63}{2}$
23 $[23, 23, -w - 3]$ $\phantom{-}1$
29 $[29, 29, -w^{2} + 2w + 4]$ $-\frac{5}{2}e^{4} + 3e^{3} + \frac{55}{2}e^{2} - \frac{31}{2}e - \frac{97}{2}$
31 $[31, 31, 2w - 3]$ $-2e^{4} + 3e^{3} + 23e^{2} - 18e - 43$
41 $[41, 41, -2w^{2} + 3w + 6]$ $\phantom{-}e^{4} - e^{3} - 12e^{2} + 5e + 22$
43 $[43, 43, w^{2} - 3w + 3]$ $-\frac{11}{4}e^{4} + 3e^{3} + \frac{127}{4}e^{2} - \frac{61}{4}e - \frac{257}{4}$
47 $[47, 47, w^{2} + w - 4]$ $\phantom{-}\frac{3}{4}e^{4} - e^{3} - \frac{35}{4}e^{2} + \frac{21}{4}e + \frac{57}{4}$
49 $[49, 7, 2w^{2} - 3w - 3]$ $\phantom{-}\frac{17}{4}e^{4} - 5e^{3} - \frac{197}{4}e^{2} + \frac{95}{4}e + \frac{395}{4}$
53 $[53, 53, w^{2} - 3w - 2]$ $-\frac{11}{4}e^{4} + 3e^{3} + \frac{127}{4}e^{2} - \frac{49}{4}e - \frac{265}{4}$
59 $[59, 59, 2w^{2} - w - 5]$ $-3e^{4} + 3e^{3} + 36e^{2} - 15e - 78$
59 $[59, 59, w^{2} - w - 7]$ $\phantom{-}4e^{4} - 6e^{3} - 43e^{2} + 33e + 75$
59 $[59, 59, -w^{2} - w + 7]$ $\phantom{-}\frac{9}{2}e^{4} - 5e^{3} - \frac{103}{2}e^{2} + \frac{51}{2}e + \frac{197}{2}$
67 $[67, 67, 2w^{2} - 3w - 7]$ $-\frac{19}{4}e^{4} + 6e^{3} + \frac{211}{4}e^{2} - \frac{125}{4}e - \frac{365}{4}$
73 $[73, 73, -w^{2} + 4w - 5]$ $\phantom{-}\frac{5}{2}e^{4} - 3e^{3} - \frac{53}{2}e^{2} + \frac{25}{2}e + \frac{99}{2}$
79 $[79, 79, w^{2} - 8]$ $\phantom{-}\frac{11}{4}e^{4} - 2e^{3} - \frac{131}{4}e^{2} + \frac{37}{4}e + \frac{261}{4}$
79 $[79, 79, w^{2} - 5w + 5]$ $-\frac{3}{2}e^{4} + 2e^{3} + \frac{31}{2}e^{2} - \frac{17}{2}e - \frac{53}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23, 23, -w - 3]$ $-1$