# Properties

 Label 4.4.5744.1-37.1-c Base field 4.4.5744.1 Weight $[2, 2, 2, 2]$ Level norm $37$ Level $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.5744.1

Generator $$w$$, with minimal polynomial $$x^{4} - 5x^{2} - 2x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ Dimension: $7$ 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:

 $$x^{7} - 8x^{6} + 9x^{5} + 62x^{4} - 136x^{3} - 62x^{2} + 285x - 139$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-\frac{21}{103}e^{6} + e^{5} + \frac{120}{103}e^{4} - \frac{960}{103}e^{3} + \frac{223}{103}e^{2} + \frac{1953}{103}e - \frac{1073}{103}$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}\frac{11}{309}e^{6} - \frac{70}{103}e^{4} - \frac{71}{309}e^{3} + \frac{342}{103}e^{2} + \frac{110}{309}e - \frac{929}{309}$
13 $[13, 13, -w^{3} + w^{2} + 4w]$ $-\frac{17}{103}e^{6} + e^{5} + \frac{53}{103}e^{4} - \frac{1042}{103}e^{3} + \frac{568}{103}e^{2} + \frac{2405}{103}e - \frac{1673}{103}$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{98}{309}e^{6} - 2e^{5} - \frac{15}{103}e^{4} + \frac{5407}{309}e^{3} - \frac{1457}{103}e^{2} - \frac{10144}{309}e + \frac{9196}{309}$
17 $[17, 17, -w^{2} + 2]$ $\phantom{-}\frac{65}{309}e^{6} - e^{5} - \frac{114}{103}e^{4} + \frac{2839}{309}e^{3} - \frac{423}{103}e^{2} - \frac{6148}{309}e + \frac{5494}{309}$
19 $[19, 19, -w^{3} + 5w]$ $-\frac{43}{309}e^{6} + e^{5} - \frac{26}{103}e^{4} - \frac{2981}{309}e^{3} + \frac{1004}{103}e^{2} + \frac{6677}{309}e - \frac{6116}{309}$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}\frac{43}{309}e^{6} - e^{5} + \frac{26}{103}e^{4} + \frac{2672}{309}e^{3} - \frac{798}{103}e^{2} - \frac{4205}{309}e + \frac{3644}{309}$
37 $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ $-1$
43 $[43, 43, -w - 3]$ $-\frac{29}{309}e^{6} + \frac{222}{103}e^{4} + \frac{131}{309}e^{3} - \frac{1426}{103}e^{2} - \frac{599}{309}e + \frac{6101}{309}$
53 $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{52}{309}e^{6} + e^{5} - \frac{53}{103}e^{4} - \frac{2024}{309}e^{3} + \frac{1183}{103}e^{2} + \frac{2879}{309}e - \frac{4148}{309}$
53 $[53, 53, w^{3} - 6w - 2]$ $\phantom{-}\frac{217}{309}e^{6} - 4e^{5} - \frac{173}{103}e^{4} + \frac{10847}{309}e^{3} - \frac{2439}{103}e^{2} - \frac{20078}{309}e + \frac{18023}{309}$
59 $[59, 59, 2w^{3} - w^{2} - 10w - 2]$ $-\frac{8}{103}e^{6} + \frac{134}{103}e^{4} + \frac{61}{103}e^{3} - \frac{381}{103}e^{2} - \frac{389}{103}e - \frac{139}{103}$
61 $[61, 61, 2w^{3} - w^{2} - 10w]$ $-\frac{16}{309}e^{6} + e^{5} - \frac{151}{103}e^{4} - \frac{3071}{309}e^{3} + \frac{982}{103}e^{2} + \frac{6329}{309}e - \frac{2750}{309}$
61 $[61, 61, 2w^{3} - w^{2} - 8w]$ $-\frac{169}{309}e^{6} + 3e^{5} + \frac{214}{103}e^{4} - \frac{8123}{309}e^{3} + \frac{935}{103}e^{2} + \frac{14996}{309}e - \frac{7301}{309}$
71 $[71, 71, 2w^{3} - 9w - 2]$ $\phantom{-}\frac{37}{309}e^{6} - e^{5} + \frac{8}{103}e^{4} + \frac{3104}{309}e^{3} - \frac{404}{103}e^{2} - \frac{6737}{309}e + \frac{1763}{309}$
73 $[73, 73, -w^{3} - w^{2} + 6w + 3]$ $\phantom{-}\frac{29}{103}e^{6} - e^{5} - \frac{254}{103}e^{4} + \frac{796}{103}e^{3} + \frac{364}{103}e^{2} - \frac{1049}{103}e + \frac{1212}{103}$
81 $[81, 3, -3]$ $-\frac{5}{309}e^{6} - \frac{15}{103}e^{4} + \frac{566}{309}e^{3} - \frac{15}{103}e^{2} - \frac{2522}{309}e + \frac{2810}{309}$
83 $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}\frac{64}{309}e^{6} - 2e^{5} + \frac{192}{103}e^{4} + \frac{5795}{309}e^{3} - \frac{2486}{103}e^{2} - \frac{12029}{309}e + \frac{14090}{309}$
101 $[101, 101, 2w^{3} - 8w - 3]$ $-\frac{59}{103}e^{6} + 3e^{5} + \frac{293}{103}e^{4} - \frac{2859}{103}e^{3} + \frac{705}{103}e^{2} + \frac{5796}{103}e - \frac{2480}{103}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ $1$