# Properties

 Base field 4.4.19225.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11,11,w + 3]$ Label 4.4.19225.1-11.2-a Dimension 7 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[11,11,w + 3]$ Label 4.4.19225.1-11.2-a Dimension 7 Is CM no Is base change no Parent newspace dimension 19

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{7} - 14x^{5} + 16x^{4} + 27x^{3} - 43x^{2} + 8x + 3$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $-\frac{2}{25}e^{6} - \frac{11}{25}e^{5} + \frac{1}{5}e^{4} + \frac{83}{25}e^{3} + \frac{3}{5}e^{2} - \frac{169}{25}e - \frac{8}{25}$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $-\frac{13}{25}e^{6} - \frac{34}{25}e^{5} + \frac{24}{5}e^{4} + \frac{152}{25}e^{3} - \frac{48}{5}e^{2} - \frac{136}{25}e + \frac{48}{25}$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}\frac{4}{5}e^{6} + \frac{7}{5}e^{5} - 9e^{4} - \frac{16}{5}e^{3} + 19e^{2} - \frac{12}{5}e - \frac{14}{5}$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-\frac{4}{25}e^{6} + \frac{3}{25}e^{5} + \frac{12}{5}e^{4} - \frac{109}{25}e^{3} - \frac{29}{5}e^{2} + \frac{287}{25}e + \frac{9}{25}$
11 $[11, 11, -w - 3]$ $\phantom{-}1$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $\phantom{-}\frac{13}{25}e^{6} + \frac{34}{25}e^{5} - \frac{24}{5}e^{4} - \frac{152}{25}e^{3} + \frac{53}{5}e^{2} + \frac{186}{25}e - \frac{198}{25}$
29 $[29, 29, w + 1]$ $\phantom{-}\frac{4}{25}e^{6} + \frac{22}{25}e^{5} - \frac{2}{5}e^{4} - \frac{141}{25}e^{3} + \frac{4}{5}e^{2} + \frac{138}{25}e - \frac{34}{25}$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}\frac{2}{5}e^{6} + \frac{1}{5}e^{5} - 6e^{4} + \frac{12}{5}e^{3} + 16e^{2} - \frac{51}{5}e - \frac{22}{5}$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}\frac{3}{5}e^{6} - \frac{1}{5}e^{5} - 9e^{4} + \frac{53}{5}e^{3} + 18e^{2} - \frac{124}{5}e + \frac{7}{5}$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-\frac{6}{25}e^{6} - \frac{8}{25}e^{5} + \frac{13}{5}e^{4} - \frac{26}{25}e^{3} - \frac{21}{5}e^{2} + \frac{168}{25}e - \frac{24}{25}$
31 $[31, 31, -w + 3]$ $\phantom{-}\frac{24}{25}e^{6} + \frac{7}{25}e^{5} - \frac{67}{5}e^{4} + \frac{279}{25}e^{3} + \frac{149}{5}e^{2} - \frac{672}{25}e - \frac{104}{25}$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-\frac{7}{5}e^{6} - \frac{6}{5}e^{5} + 19e^{4} - \frac{27}{5}e^{3} - 46e^{2} + \frac{101}{5}e + \frac{47}{5}$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}\frac{7}{25}e^{6} - \frac{24}{25}e^{5} - \frac{31}{5}e^{4} + \frac{322}{25}e^{3} + \frac{72}{5}e^{2} - \frac{646}{25}e + \frac{28}{25}$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $-\frac{28}{25}e^{6} - \frac{29}{25}e^{5} + \frac{69}{5}e^{4} - \frac{113}{25}e^{3} - \frac{138}{5}e^{2} + \frac{434}{25}e + \frac{63}{25}$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $-\frac{22}{25}e^{6} - \frac{21}{25}e^{5} + \frac{56}{5}e^{4} - \frac{87}{25}e^{3} - \frac{112}{5}e^{2} + \frac{391}{25}e - \frac{88}{25}$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-\frac{14}{25}e^{6} - \frac{27}{25}e^{5} + \frac{32}{5}e^{4} + \frac{81}{25}e^{3} - \frac{89}{5}e^{2} + \frac{42}{25}e + \frac{194}{25}$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}\frac{43}{25}e^{6} + \frac{49}{25}e^{5} - \frac{104}{5}e^{4} + \frac{153}{25}e^{3} + \frac{223}{5}e^{2} - \frac{654}{25}e - \frac{178}{25}$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}\frac{14}{25}e^{6} + \frac{27}{25}e^{5} - \frac{22}{5}e^{4} + \frac{44}{25}e^{3} + \frac{4}{5}e^{2} - \frac{417}{25}e + \frac{306}{25}$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $-\frac{64}{25}e^{6} - \frac{52}{25}e^{5} + \frac{172}{5}e^{4} - \frac{294}{25}e^{3} - \frac{394}{5}e^{2} + \frac{1017}{25}e + \frac{294}{25}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11,11,w + 3]$ $-1$