Base field 6.6.1134389.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 6x^{3} + 4x^{2} - 3x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 63x^{8} + 1440x^{6} - 14284x^{4} + 54806x^{2} - 31104\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{763}{9649188}e^{9} + \frac{3729}{1072132}e^{7} - \frac{19117}{268033}e^{5} + \frac{2595811}{2412297}e^{3} - \frac{34903687}{4824594}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 3w]$ | $\phantom{-}\frac{5083}{9649188}e^{9} - \frac{33273}{1072132}e^{7} + \frac{154404}{268033}e^{5} - \frac{7934611}{2412297}e^{3} - \frac{2111099}{4824594}e$ |
| 19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $-\frac{16313}{9649188}e^{9} + \frac{95183}{1072132}e^{7} - \frac{413641}{268033}e^{5} + \frac{23063840}{2412297}e^{3} - \frac{57964337}{4824594}e$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}4$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ | $-\frac{2203}{3216396}e^{9} + \frac{40731}{1072132}e^{7} - \frac{192638}{268033}e^{5} + \frac{4375411}{804099}e^{3} - \frac{22565425}{1608198}e$ |
| 31 | $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ | $\phantom{-}\frac{1163}{1072132}e^{9} - \frac{58181}{1072132}e^{7} + \frac{240120}{268033}e^{5} - \frac{1392602}{268033}e^{3} + \frac{2260795}{536066}e$ |
| 37 | $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $-1$ |
| 37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ | $\phantom{-}0$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + w - 3]$ | $\phantom{-}\frac{663}{268033}e^{8} - \frac{27406}{268033}e^{6} + \frac{352112}{268033}e^{4} - \frac{1669232}{268033}e^{2} + \frac{3574656}{268033}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{2666}{268033}e^{8} - \frac{137289}{268033}e^{6} + \frac{2259601}{268033}e^{4} - \frac{11928106}{268033}e^{2} + \frac{3886861}{268033}$ |
| 67 | $[67, 67, 2w - 1]$ | $-\frac{1903}{268033}e^{8} + \frac{103728}{268033}e^{6} - \frac{1839422}{268033}e^{4} + \frac{11194050}{268033}e^{2} - \frac{10468892}{268033}$ |
| 79 | $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ | $-\frac{917}{3216396}e^{9} + \frac{23281}{1072132}e^{7} - \frac{145156}{268033}e^{5} + \frac{3768917}{804099}e^{3} - \frac{14225495}{1608198}e$ |
| 79 | $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ | $-\frac{4739}{9649188}e^{9} + \frac{42833}{1072132}e^{7} - \frac{271195}{268033}e^{5} + \frac{22429988}{2412297}e^{3} - \frac{117993599}{4824594}e$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ | $\phantom{-}\frac{1423}{268033}e^{8} - \frac{74184}{268033}e^{6} + \frac{1298274}{268033}e^{4} - \frac{8285184}{268033}e^{2} + \frac{9581278}{268033}$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ | $\phantom{-}\frac{8941}{9649188}e^{9} - \frac{50723}{1072132}e^{7} + \frac{201886}{268033}e^{5} - \frac{7341796}{2412297}e^{3} - \frac{49460219}{4824594}e$ |
| 101 | $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ | $-\frac{8941}{4824594}e^{9} + \frac{50723}{536066}e^{7} - \frac{403772}{268033}e^{5} + \frac{17095889}{2412297}e^{3} + \frac{8451170}{2412297}e$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ | $\phantom{-}\frac{17479}{4824594}e^{9} - \frac{100179}{536066}e^{7} + \frac{836530}{268033}e^{5} - \frac{42755540}{2412297}e^{3} + \frac{40395139}{2412297}e$ |
| 103 | $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ | $-\frac{2786}{804099}e^{9} + \frac{48225}{268033}e^{7} - \frac{798296}{268033}e^{5} + \frac{12521306}{804099}e^{3} - \frac{222286}{804099}e$ |
| 107 | $[107, 107, w^{2} - 2w - 3]$ | $-\frac{114}{14107}e^{8} + \frac{5606}{14107}e^{6} - \frac{86907}{14107}e^{4} + \frac{422470}{14107}e^{2} + \frac{444}{14107}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37,37,-w^{5}+3w^{4}+2w^{3}-8w^{2}-w+3]$ | $1$ |