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:
\(x^{7} + 8x^{6} + 9x^{5} - 62x^{4} - 136x^{3} + 62x^{2} + 285x + 139\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{3} + 4w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{21}{103}e^{6} + e^{5} - \frac{120}{103}e^{4} - \frac{960}{103}e^{3} - \frac{223}{103}e^{2} + \frac{1953}{103}e + \frac{1073}{103}$ |
7 | $[7, 7, -w^{2} + w + 2]$ | $-\frac{11}{309}e^{6} + \frac{70}{103}e^{4} - \frac{71}{309}e^{3} - \frac{342}{103}e^{2} + \frac{110}{309}e + \frac{929}{309}$ |
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 | $[13, 13, -w^{2} + 3]$ | $-\frac{98}{309}e^{6} - 2e^{5} + \frac{15}{103}e^{4} + \frac{5407}{309}e^{3} + \frac{1457}{103}e^{2} - \frac{10144}{309}e - \frac{9196}{309}$ |
17 | $[17, 17, -w^{2} + 2]$ | $-\frac{65}{309}e^{6} - e^{5} + \frac{114}{103}e^{4} + \frac{2839}{309}e^{3} + \frac{423}{103}e^{2} - \frac{6148}{309}e - \frac{5494}{309}$ |
19 | $[19, 19, -w^{3} + 5w]$ | $\phantom{-}\frac{43}{309}e^{6} + e^{5} + \frac{26}{103}e^{4} - \frac{2981}{309}e^{3} - \frac{1004}{103}e^{2} + \frac{6677}{309}e + \frac{6116}{309}$ |
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 | $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ | $\phantom{-}1$ |
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 | $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{52}{309}e^{6} + e^{5} + \frac{53}{103}e^{4} - \frac{2024}{309}e^{3} - \frac{1183}{103}e^{2} + \frac{2879}{309}e + \frac{4148}{309}$ |
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 | $[61, 61, 2w^{3} - w^{2} - 8w]$ | $\phantom{-}\frac{169}{309}e^{6} + 3e^{5} - \frac{214}{103}e^{4} - \frac{8123}{309}e^{3} - \frac{935}{103}e^{2} + \frac{14996}{309}e + \frac{7301}{309}$ |
71 | $[71, 71, 2w^{3} - 9w - 2]$ | $-\frac{37}{309}e^{6} - e^{5} - \frac{8}{103}e^{4} + \frac{3104}{309}e^{3} + \frac{404}{103}e^{2} - \frac{6737}{309}e - \frac{1763}{309}$ |
73 | $[73, 73, -w^{3} - w^{2} + 6w + 3]$ | $-\frac{29}{103}e^{6} - e^{5} + \frac{254}{103}e^{4} + \frac{796}{103}e^{3} - \frac{364}{103}e^{2} - \frac{1049}{103}e - \frac{1212}{103}$ |
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 | $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ | $-\frac{64}{309}e^{6} - 2e^{5} - \frac{192}{103}e^{4} + \frac{5795}{309}e^{3} + \frac{2486}{103}e^{2} - \frac{12029}{309}e - \frac{14090}{309}$ |
101 | $[101, 101, 2w^{3} - 8w - 3]$ | $\phantom{-}\frac{59}{103}e^{6} + 3e^{5} - \frac{293}{103}e^{4} - \frac{2859}{103}e^{3} - \frac{705}{103}e^{2} + \frac{5796}{103}e + \frac{2480}{103}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$37$ | $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ | $-1$ |