# Properties

 Label 4.4.18097.1-12.1-f Base field 4.4.18097.1 Weight $[2, 2, 2, 2]$ Level norm $12$ Level $[12, 6, -w - 2]$ Dimension $6$ 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: $[12, 6, -w - 2]$ Dimension: $6$ 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:

 $$x^{6} + 2x^{5} - 13x^{4} - 22x^{3} + 29x^{2} + 24x + 3$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $-1$
4 $[4, 2, w]$ $-1$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{13}{2}e^{3} + \frac{21}{2}e^{2} - 15e - \frac{13}{2}$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e - \frac{3}{2}$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 7e^{3} + 5e^{2} - \frac{37}{2}e - \frac{5}{2}$
27 $[27, 3, -w^{3} + 7w + 1]$ $\phantom{-}e^{5} + \frac{3}{2}e^{4} - \frac{27}{2}e^{3} - \frac{31}{2}e^{2} + \frac{71}{2}e + 13$
31 $[31, 31, w + 3]$ $-\frac{1}{2}e^{5} - e^{4} + 7e^{3} + 11e^{2} - \frac{35}{2}e - 9$
31 $[31, 31, -w^{2} + 5]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e - \frac{1}{2}$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}e^{5} + \frac{3}{2}e^{4} - 13e^{3} - 16e^{2} + 29e + \frac{27}{2}$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $\phantom{-}\frac{1}{2}e^{5} + e^{4} - 7e^{3} - 11e^{2} + \frac{39}{2}e + 9$
47 $[47, 47, w^{3} - 5w - 3]$ $\phantom{-}\frac{1}{2}e^{4} - 4e^{2} + e + \frac{1}{2}$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $-e^{5} - 2e^{4} + \frac{25}{2}e^{3} + \frac{41}{2}e^{2} - \frac{51}{2}e - \frac{29}{2}$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}e^{5} + 2e^{4} - 13e^{3} - 22e^{2} + 30e + 20$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - 6e^{3} - 4e^{2} + \frac{23}{2}e - \frac{5}{2}$
83 $[83, 83, -w^{3} + 5w + 1]$ $\phantom{-}\frac{1}{2}e^{5} + e^{4} - 8e^{3} - 12e^{2} + \frac{57}{2}e + 16$
83 $[83, 83, 2w - 1]$ $\phantom{-}e^{5} + 2e^{4} - \frac{27}{2}e^{3} - \frac{41}{2}e^{2} + \frac{67}{2}e + \frac{31}{2}$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{11}{2}e + \frac{7}{2}$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} - \frac{1}{2}e^{2} + 17e + \frac{19}{2}$
89 $[89, 89, w^{3} - 5w + 5]$ $-2e^{5} - \frac{5}{2}e^{4} + 27e^{3} + 27e^{2} - 66e - \frac{39}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 1]$ $1$
$4$ $[4, 2, w]$ $1$