Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[3, 3, w]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} - 3x^{6} - 11x^{5} + 42x^{4} - 7x^{3} - 76x^{2} + 56x - 7\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $-1$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $\phantom{-}\frac{17}{83}e^{6} + \frac{5}{83}e^{5} - \frac{234}{83}e^{4} - \frac{8}{83}e^{3} + \frac{670}{83}e^{2} + \frac{129}{83}e - \frac{327}{83}$ |
5 | $[5, 5, w + 1]$ | $-\frac{45}{83}e^{6} + \frac{60}{83}e^{5} + \frac{595}{83}e^{4} - \frac{926}{83}e^{3} - \frac{1173}{83}e^{2} + \frac{1714}{83}e - \frac{106}{83}$ |
5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{57}{83}e^{6} - \frac{76}{83}e^{5} - \frac{726}{83}e^{4} + \frac{1184}{83}e^{3} + \frac{1187}{83}e^{2} - \frac{2160}{83}e + \frac{588}{83}$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{56}{83}e^{6} - \frac{47}{83}e^{5} - \frac{722}{83}e^{4} + \frac{789}{83}e^{3} + \frac{1338}{83}e^{2} - \frac{1279}{83}e + \frac{534}{83}$ |
11 | $[11, 11, w + 9]$ | $\phantom{-}\frac{56}{83}e^{6} - \frac{47}{83}e^{5} - \frac{722}{83}e^{4} + \frac{789}{83}e^{3} + \frac{1421}{83}e^{2} - \frac{1113}{83}e - \frac{130}{83}$ |
17 | $[17, 17, w + 2]$ | $\phantom{-}\frac{21}{83}e^{6} - \frac{28}{83}e^{5} - \frac{250}{83}e^{4} + \frac{410}{83}e^{3} + \frac{232}{83}e^{2} - \frac{490}{83}e + \frac{221}{83}$ |
17 | $[17, 17, w + 14]$ | $\phantom{-}\frac{21}{83}e^{6} - \frac{28}{83}e^{5} - \frac{250}{83}e^{4} + \frac{410}{83}e^{3} + \frac{232}{83}e^{2} - \frac{407}{83}e + \frac{553}{83}$ |
19 | $[19, 19, w]$ | $-\frac{54}{83}e^{6} + \frac{72}{83}e^{5} + \frac{714}{83}e^{4} - \frac{1078}{83}e^{3} - \frac{1391}{83}e^{2} + \frac{1924}{83}e - \frac{260}{83}$ |
19 | $[19, 19, w + 18]$ | $-\frac{3}{83}e^{6} + \frac{4}{83}e^{5} + \frac{12}{83}e^{4} - \frac{106}{83}e^{3} + \frac{204}{83}e^{2} + \frac{236}{83}e - \frac{245}{83}$ |
37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{13}{83}e^{6} - \frac{45}{83}e^{5} - \frac{135}{83}e^{4} + \frac{653}{83}e^{3} - \frac{220}{83}e^{2} - \frac{1327}{83}e + \frac{1117}{83}$ |
37 | $[37, 37, w - 5]$ | $-\frac{89}{83}e^{6} + \frac{91}{83}e^{5} + \frac{1186}{83}e^{4} - \frac{1457}{83}e^{3} - \frac{2497}{83}e^{2} + \frac{2713}{83}e - \frac{241}{83}$ |
43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{84}{83}e^{6} - \frac{195}{83}e^{5} - \frac{1000}{83}e^{4} + \frac{2802}{83}e^{3} + \frac{762}{83}e^{2} - \frac{5114}{83}e + \frac{1548}{83}$ |
43 | $[43, 43, w + 26]$ | $-\frac{13}{83}e^{6} + \frac{45}{83}e^{5} + \frac{135}{83}e^{4} - \frac{653}{83}e^{3} + \frac{137}{83}e^{2} + \frac{1161}{83}e - \frac{370}{83}$ |
49 | $[49, 7, -7]$ | $-\frac{79}{83}e^{6} + \frac{133}{83}e^{5} + \frac{980}{83}e^{4} - \frac{1989}{83}e^{3} - \frac{1268}{83}e^{2} + \frac{3697}{83}e - \frac{1527}{83}$ |
53 | $[53, 53, -w - 10]$ | $-\frac{41}{83}e^{6} + \frac{110}{83}e^{5} + \frac{496}{83}e^{4} - \frac{1504}{83}e^{3} - \frac{366}{83}e^{2} + \frac{2506}{83}e - \frac{803}{83}$ |
53 | $[53, 53, w - 11]$ | $\phantom{-}\frac{107}{83}e^{6} - \frac{198}{83}e^{5} - \frac{1341}{83}e^{4} + \frac{2923}{83}e^{3} + \frac{1771}{83}e^{2} - \frac{5623}{83}e + \frac{1794}{83}$ |
61 | $[61, 61, w + 15]$ | $-\frac{124}{83}e^{6} + \frac{193}{83}e^{5} + \frac{1575}{83}e^{4} - \frac{2832}{83}e^{3} - \frac{2441}{83}e^{2} + \frac{4664}{83}e - \frac{1135}{83}$ |
61 | $[61, 61, w + 45]$ | $-\frac{73}{83}e^{6} + \frac{125}{83}e^{5} + \frac{873}{83}e^{4} - \frac{1943}{83}e^{3} - \frac{929}{83}e^{2} + \frac{3972}{83}e - \frac{1120}{83}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $1$ |