# Properties

 Label 4.4.12725.1-19.1-e Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, w^{2} - 2w - 5]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19, 19, w^{2} - 2w - 5]$ Dimension: $8$ 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:

 $$x^{8} - 24x^{7} + 232x^{6} - 1156x^{5} + 3149x^{4} - 4522x^{3} + 2741x^{2} + 214x - 639$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $-\frac{1}{2}e^{7} + \frac{155}{14}e^{6} - \frac{1339}{14}e^{5} + \frac{5653}{14}e^{4} - 845e^{3} + \frac{5207}{7}e^{2} - \frac{555}{14}e - \frac{2549}{14}$
11 $[11, 11, w^{2} - 5]$ $-\frac{13}{98}e^{7} + \frac{281}{98}e^{6} - \frac{2361}{98}e^{5} + \frac{9609}{98}e^{4} - \frac{9479}{49}e^{3} + \frac{7332}{49}e^{2} + \frac{129}{14}e - \frac{3629}{98}$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}e$
11 $[11, 11, w - 2]$ $\phantom{-}\frac{95}{98}e^{7} - \frac{2103}{98}e^{6} + \frac{18129}{98}e^{5} - \frac{76147}{98}e^{4} + \frac{78900}{49}e^{3} - \frac{68336}{49}e^{2} + \frac{983}{14}e + \frac{32223}{98}$
16 $[16, 2, 2]$ $\phantom{-}\frac{45}{98}e^{7} - \frac{977}{98}e^{6} + \frac{8219}{98}e^{5} - \frac{33445}{98}e^{4} + \frac{33219}{49}e^{3} - \frac{27102}{49}e^{2} + \frac{27}{2}e + \frac{12129}{98}$
19 $[19, 19, w^{2} - 2w - 5]$ $-1$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}\frac{121}{98}e^{7} - \frac{2679}{98}e^{6} + \frac{23075}{98}e^{5} - \frac{96695}{98}e^{4} + \frac{99720}{49}e^{3} - \frac{85534}{49}e^{2} + \frac{1009}{14}e + \frac{40671}{98}$
25 $[25, 5, -2w^{2} + 2w + 11]$ $-\frac{101}{98}e^{7} + \frac{2223}{98}e^{6} - \frac{19041}{98}e^{5} + \frac{79435}{98}e^{4} - \frac{81771}{49}e^{3} + \frac{70418}{49}e^{2} - \frac{883}{14}e - \frac{34235}{98}$
29 $[29, 29, w]$ $\phantom{-}\frac{3}{14}e^{7} - \frac{9}{2}e^{6} + \frac{73}{2}e^{5} - \frac{1999}{14}e^{4} + \frac{1908}{7}e^{3} - \frac{1514}{7}e^{2} + \frac{125}{14}e + \frac{687}{14}$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}\frac{61}{98}e^{7} - \frac{1353}{98}e^{6} + \frac{11645}{98}e^{5} - \frac{48611}{98}e^{4} + \frac{49793}{49}e^{3} - \frac{42447}{49}e^{2} + \frac{559}{14}e + \frac{19543}{98}$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-\frac{13}{49}e^{7} + \frac{288}{49}e^{6} - \frac{2473}{49}e^{5} + \frac{10274}{49}e^{4} - \frac{20820}{49}e^{3} + \frac{17198}{49}e^{2} - \frac{27}{7}e - \frac{3832}{49}$
29 $[29, 29, w - 1]$ $-\frac{75}{98}e^{7} + \frac{1647}{98}e^{6} - \frac{14095}{98}e^{5} + \frac{58887}{98}e^{4} - \frac{60951}{49}e^{3} + \frac{53220}{49}e^{2} - \frac{857}{14}e - \frac{25787}{98}$
31 $[31, 31, w^{3} - 6w - 6]$ $-\frac{23}{98}e^{7} + \frac{523}{98}e^{6} - \frac{4651}{98}e^{5} + \frac{20255}{98}e^{4} - \frac{21859}{49}e^{3} + \frac{19678}{49}e^{2} - \frac{281}{14}e - \frac{9115}{98}$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $-\frac{141}{98}e^{7} + \frac{3135}{98}e^{6} - \frac{27109}{98}e^{5} + \frac{114053}{98}e^{4} - \frac{118257}{49}e^{3} + \frac{102708}{49}e^{2} - \frac{1583}{14}e - \frac{48675}{98}$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $\phantom{-}\frac{97}{98}e^{7} - \frac{2143}{98}e^{6} + \frac{18433}{98}e^{5} - \frac{77243}{98}e^{4} + \frac{79857}{49}e^{3} - \frac{69030}{49}e^{2} + \frac{139}{2}e + \frac{32763}{98}$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $-\frac{75}{49}e^{7} + \frac{1661}{49}e^{6} - \frac{14319}{49}e^{5} + \frac{60119}{49}e^{4} - \frac{124450}{49}e^{3} + \frac{107392}{49}e^{2} - 97e - \frac{25605}{49}$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{8}{7}e^{7} - \frac{178}{7}e^{6} + \frac{1546}{7}e^{5} - \frac{6563}{7}e^{4} + \frac{13802}{7}e^{3} - 1743e^{2} + \frac{708}{7}e + \frac{2927}{7}$
59 $[59, 59, 2w^{2} - w - 13]$ $-\frac{11}{49}e^{7} + \frac{248}{49}e^{6} - \frac{2169}{49}e^{5} + \frac{9178}{49}e^{4} - \frac{18906}{49}e^{3} + \frac{15712}{49}e^{2} + \frac{47}{7}e - \frac{3978}{49}$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $-\frac{11}{7}e^{7} + \frac{242}{7}e^{6} - \frac{2073}{7}e^{5} + \frac{8650}{7}e^{4} - \frac{17793}{7}e^{3} + \frac{15234}{7}e^{2} - \frac{590}{7}e - \frac{3678}{7}$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{44}{49}e^{7} - \frac{978}{49}e^{6} + \frac{8452}{49}e^{5} - \frac{35529}{49}e^{4} + \frac{73566}{49}e^{3} - \frac{63562}{49}e^{2} + \frac{410}{7}e + \frac{15310}{49}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, w^{2} - 2w - 5]$ $1$