# Properties

 Base field 4.4.18688.1 Weight [2, 2, 2, 2] Level norm 14 Level $[14,14,\frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + \frac{2}{3}]$ Label 4.4.18688.1-14.2-d Dimension 7 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18688.1

Generator $$w$$, with minimal polynomial $$x^{4} - 10x^{2} - 4x + 14$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[14,14,\frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + \frac{2}{3}]$ Label 4.4.18688.1-14.2-d Dimension 7 Is CM no Is base change no Parent newspace dimension 18

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{7}$$ $$\mathstrut +\mathstrut 3x^{6}$$ $$\mathstrut -\mathstrut 22x^{5}$$ $$\mathstrut -\mathstrut 61x^{4}$$ $$\mathstrut +\mathstrut 92x^{3}$$ $$\mathstrut +\mathstrut 218x^{2}$$ $$\mathstrut -\mathstrut 100x$$ $$\mathstrut -\mathstrut 172$$
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $-1$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}\frac{107}{6722}e^{6} + \frac{367}{6722}e^{5} - \frac{784}{3361}e^{4} - \frac{5819}{6722}e^{3} - \frac{2454}{3361}e^{2} + \frac{1059}{3361}e + \frac{13952}{3361}$
9 $[9, 3, w + 1]$ $-\frac{44}{3361}e^{6} - \frac{773}{6722}e^{5} + \frac{253}{6722}e^{4} + \frac{7827}{3361}e^{3} + \frac{21721}{6722}e^{2} - \frac{21728}{3361}e - \frac{18919}{3361}$
17 $[17, 17, w + 3]$ $-\frac{47}{3361}e^{6} - \frac{291}{6722}e^{5} + \frac{2791}{6722}e^{4} + \frac{3090}{3361}e^{3} - \frac{22859}{6722}e^{2} - \frac{10071}{3361}e + \frac{23866}{3361}$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $-\frac{175}{3361}e^{6} - \frac{506}{3361}e^{5} + \frac{3444}{3361}e^{4} + \frac{9360}{3361}e^{3} - \frac{6265}{3361}e^{2} - \frac{21337}{3361}e - \frac{10394}{3361}$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $-\frac{19}{6722}e^{6} + \frac{203}{3361}e^{5} + \frac{1315}{6722}e^{4} - \frac{9835}{6722}e^{3} - \frac{16813}{6722}e^{2} + \frac{27391}{3361}e + \frac{18411}{3361}$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $-\frac{243}{6722}e^{6} - \frac{645}{6722}e^{5} + \frac{2660}{3361}e^{4} + \frac{12901}{6722}e^{3} - \frac{12080}{3361}e^{2} - \frac{20278}{3361}e + \frac{17002}{3361}$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $-\frac{262}{3361}e^{6} - \frac{239}{3361}e^{5} + \frac{6635}{3361}e^{4} + \frac{3066}{3361}e^{3} - \frac{40973}{3361}e^{2} + \frac{4143}{3361}e + \frac{70826}{3361}$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}\frac{91}{3361}e^{6} + \frac{532}{3361}e^{5} - \frac{1522}{3361}e^{4} - \frac{10917}{3361}e^{3} + \frac{569}{3361}e^{2} + \frac{35160}{3361}e + \frac{11858}{3361}$
41 $[41, 41, 2w + 3]$ $\phantom{-}\frac{417}{6722}e^{6} + \frac{111}{6722}e^{5} - \frac{5851}{3361}e^{4} - \frac{313}{6722}e^{3} + \frac{40066}{3361}e^{2} - \frac{5202}{3361}e - \frac{44446}{3361}$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $-\frac{953}{6722}e^{6} - \frac{1493}{3361}e^{5} + \frac{19965}{6722}e^{4} + \frac{54717}{6722}e^{3} - \frac{66383}{6722}e^{2} - \frac{54727}{3361}e + \frac{19348}{3361}$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $\phantom{-}\frac{129}{3361}e^{6} - \frac{280}{3361}e^{5} - \frac{4152}{3361}e^{4} + \frac{5392}{3361}e^{3} + \frac{34195}{3361}e^{2} - \frac{10545}{3361}e - \frac{41620}{3361}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $\phantom{-}\frac{19}{6722}e^{6} - \frac{203}{3361}e^{5} - \frac{1315}{6722}e^{4} + \frac{9835}{6722}e^{3} + \frac{16813}{6722}e^{2} - \frac{24030}{3361}e - \frac{15050}{3361}$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $\phantom{-}\frac{47}{3361}e^{6} + \frac{291}{6722}e^{5} - \frac{2791}{6722}e^{4} - \frac{3090}{3361}e^{3} + \frac{22859}{6722}e^{2} + \frac{13432}{3361}e - \frac{13783}{3361}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $-\frac{317}{6722}e^{6} - \frac{151}{3361}e^{5} + \frac{6373}{6722}e^{4} + \frac{3607}{6722}e^{3} - \frac{12693}{6722}e^{2} + \frac{6977}{3361}e - \frac{8761}{3361}$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $\phantom{-}\frac{55}{6722}e^{6} + \frac{63}{6722}e^{5} + \frac{131}{3361}e^{4} - \frac{541}{6722}e^{3} - \frac{10779}{3361}e^{2} - \frac{3225}{3361}e + \frac{24008}{3361}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $\phantom{-}\frac{374}{3361}e^{6} + \frac{1529}{6722}e^{5} - \frac{17275}{6722}e^{4} - \frac{14434}{3361}e^{3} + \frac{82571}{6722}e^{2} + \frac{33443}{3361}e - \frac{35807}{3361}$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $-\frac{592}{3361}e^{6} - \frac{617}{3361}e^{5} + \frac{15146}{3361}e^{4} + \frac{9673}{3361}e^{3} - \frac{89758}{3361}e^{2} - \frac{17655}{3361}e + \frac{112108}{3361}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{8}{3}]$ $1$
7 $[7,7,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $1$