# Properties

 Label 4.4.18432.1-14.1-e Base field 4.4.18432.1 Weight $[2, 2, 2, 2]$ Level norm $14$ Level $[14, 14, w + 2]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18432.1

Generator $$w$$, with minimal polynomial $$x^{4} - 12x^{2} + 18$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[14, 14, w + 2]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} + 4x^{5} - 14x^{4} - 60x^{3} - 19x^{2} + 72x + 44$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $-1$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{7}{20}e^{4} - \frac{29}{20}e^{3} - \frac{103}{20}e^{2} - \frac{19}{20}e + \frac{53}{10}$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $\phantom{-}1$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $\phantom{-}\frac{1}{5}e^{5} + \frac{9}{20}e^{4} - \frac{73}{20}e^{3} - \frac{121}{20}e^{2} + \frac{147}{20}e + \frac{61}{10}$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}e$
9 $[9, 3, w - 3]$ $-\frac{1}{5}e^{5} - \frac{9}{20}e^{4} + \frac{73}{20}e^{3} + \frac{121}{20}e^{2} - \frac{147}{20}e - \frac{81}{10}$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}\frac{3}{20}e^{5} + \frac{2}{5}e^{4} - \frac{14}{5}e^{3} - \frac{61}{10}e^{2} + \frac{149}{20}e + \frac{87}{10}$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}\frac{3}{20}e^{5} + \frac{2}{5}e^{4} - \frac{14}{5}e^{3} - \frac{61}{10}e^{2} + \frac{149}{20}e + \frac{87}{10}$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $\phantom{-}\frac{1}{20}e^{5} + \frac{1}{20}e^{4} - \frac{17}{20}e^{3} + \frac{1}{20}e^{2} - \frac{21}{10}e - \frac{28}{5}$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{7}{20}e^{4} - \frac{39}{20}e^{3} - \frac{103}{20}e^{2} + \frac{131}{20}e + \frac{53}{10}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}\frac{3}{20}e^{5} + \frac{3}{20}e^{4} - \frac{51}{20}e^{3} + \frac{3}{20}e^{2} + \frac{27}{10}e - \frac{54}{5}$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $-\frac{1}{5}e^{5} - \frac{7}{10}e^{4} + \frac{17}{5}e^{3} + \frac{103}{10}e^{2} - \frac{33}{5}e - \frac{58}{5}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-\frac{13}{20}e^{5} - \frac{33}{20}e^{4} + \frac{231}{20}e^{3} + \frac{447}{20}e^{2} - \frac{106}{5}e - \frac{141}{5}$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}\frac{9}{20}e^{5} + \frac{6}{5}e^{4} - \frac{79}{10}e^{3} - \frac{163}{10}e^{2} + \frac{257}{20}e + \frac{151}{10}$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $-\frac{3}{5}e^{5} - \frac{21}{10}e^{4} + \frac{97}{10}e^{3} + \frac{309}{10}e^{2} - \frac{83}{10}e - \frac{179}{5}$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}\frac{2}{5}e^{5} + \frac{7}{5}e^{4} - \frac{34}{5}e^{3} - \frac{103}{5}e^{2} + \frac{46}{5}e + \frac{76}{5}$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-\frac{19}{20}e^{5} - \frac{59}{20}e^{4} + \frac{313}{20}e^{3} + \frac{821}{20}e^{2} - \frac{88}{5}e - \frac{183}{5}$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-\frac{7}{10}e^{5} - \frac{39}{20}e^{4} + \frac{233}{20}e^{3} + \frac{531}{20}e^{2} - \frac{217}{20}e - \frac{221}{10}$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $-\frac{9}{20}e^{5} - \frac{29}{20}e^{4} + \frac{143}{20}e^{3} + \frac{411}{20}e^{2} - \frac{28}{5}e - \frac{93}{5}$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $\phantom{-}\frac{13}{20}e^{5} + \frac{43}{20}e^{4} - \frac{211}{20}e^{3} - \frac{617}{20}e^{2} + \frac{61}{5}e + \frac{161}{5}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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