# Properties

 Label 4.4.18097.1-12.2-e Base field 4.4.18097.1 Weight $[2, 2, 2, 2]$ Level norm $12$ Level $[12, 6, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w]$ Dimension $5$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18097.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 6x + 4$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[12, 6, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $16$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{5} + 5x^{4} - 5x^{3} - 51x^{2} - 54x - 4$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $-1$
4 $[4, 2, w]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $-1$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-e^{4} - 2e^{3} + 10e^{2} + 19e + 4$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{11}{2}e^{2} - \frac{11}{2}e + 2$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $-e^{4} - e^{3} + 11e^{2} + 9e - 4$
27 $[27, 3, -w^{3} + 7w + 1]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - \frac{7}{2}e^{2} - \frac{29}{2}e - 10$
31 $[31, 31, w + 3]$ $-\frac{3}{2}e^{4} - \frac{5}{2}e^{3} + \frac{31}{2}e^{2} + \frac{47}{2}e + 3$
31 $[31, 31, -w^{2} + 5]$ $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{11}{2}e^{2} + \frac{31}{2}e + 1$
37 $[37, 37, w^{2} - 3]$ $-e^{4} - 2e^{3} + 9e^{2} + 18e + 10$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{7}{2}e - 5$
47 $[47, 47, w^{3} - 5w - 3]$ $-\frac{5}{2}e^{4} - \frac{9}{2}e^{3} + \frac{53}{2}e^{2} + \frac{91}{2}e + 5$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $-e^{3} + 11e + 4$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}\frac{5}{2}e^{4} + \frac{11}{2}e^{3} - \frac{51}{2}e^{2} - \frac{113}{2}e - 10$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}\frac{3}{2}e^{4} + \frac{3}{2}e^{3} - \frac{35}{2}e^{2} - \frac{31}{2}e + 6$
83 $[83, 83, -w^{3} + 5w + 1]$ $-3e^{4} - 6e^{3} + 30e^{2} + 59e + 18$
83 $[83, 83, 2w - 1]$ $\phantom{-}e^{3} - 9e - 4$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $-\frac{3}{2}e^{4} - \frac{3}{2}e^{3} + \frac{31}{2}e^{2} + \frac{29}{2}e + 7$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $-e^{4} - e^{3} + 12e^{2} + 10e - 12$
89 $[89, 89, w^{3} - 5w + 5]$ $-\frac{5}{2}e^{4} - \frac{5}{2}e^{3} + \frac{57}{2}e^{2} + \frac{51}{2}e - 13$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 1]$ $1$
$4$ $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $1$