Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + x^{5} + 3x^{4} + 5x^{2} + 2x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $-\frac{2}{13}e^{5} - \frac{6}{13}e^{4} - \frac{5}{13}e^{3} - \frac{10}{13}e^{2} - \frac{4}{13}e - \frac{12}{13}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{6}{13}e^{5} + \frac{5}{13}e^{4} + \frac{15}{13}e^{3} - \frac{9}{13}e^{2} + \frac{25}{13}e + \frac{10}{13}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{2}{13}e^{5} + \frac{6}{13}e^{4} + \frac{5}{13}e^{3} - \frac{3}{13}e^{2} + \frac{4}{13}e - \frac{1}{13}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{25}{13}e^{5} + \frac{23}{13}e^{4} + \frac{69}{13}e^{3} - \frac{18}{13}e^{2} + \frac{115}{13}e + \frac{46}{13}$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{20}{13}e^{5} + \frac{8}{13}e^{4} + \frac{50}{13}e^{3} - \frac{30}{13}e^{2} + \frac{118}{13}e - \frac{10}{13}$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{7}{13}e^{5} + \frac{8}{13}e^{4} + \frac{24}{13}e^{3} + \frac{22}{13}e^{2} + \frac{40}{13}e + \frac{16}{13}$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{2}{13}e^{5} - \frac{6}{13}e^{4} - \frac{5}{13}e^{3} + \frac{3}{13}e^{2} + \frac{35}{13}e + \frac{1}{13}$ |
| 13 | $[13, 13, w + 12]$ | $\phantom{-}\frac{9}{13}e^{5} + \frac{14}{13}e^{4} + \frac{42}{13}e^{3} + \frac{32}{13}e^{2} + \frac{70}{13}e + \frac{28}{13}$ |
| 43 | $[43, 43, -w - 6]$ | $\phantom{-}\frac{11}{13}e^{5} + \frac{33}{13}e^{4} + \frac{60}{13}e^{3} + \frac{55}{13}e^{2} + \frac{22}{13}e + \frac{118}{13}$ |
| 43 | $[43, 43, w - 6]$ | $-\frac{1}{13}e^{5} - \frac{3}{13}e^{4} + \frac{17}{13}e^{3} - \frac{5}{13}e^{2} - \frac{2}{13}e - \frac{110}{13}$ |
| 47 | $[47, 47, w + 19]$ | $-\frac{44}{13}e^{5} - \frac{2}{13}e^{4} - \frac{110}{13}e^{3} + \frac{66}{13}e^{2} - \frac{257}{13}e + \frac{22}{13}$ |
| 47 | $[47, 47, w + 28]$ | $-\frac{3}{13}e^{5} - \frac{9}{13}e^{4} - \frac{27}{13}e^{3} - \frac{15}{13}e^{2} - \frac{45}{13}e - \frac{18}{13}$ |
| 59 | $[59, 59, w + 16]$ | $\phantom{-}\frac{14}{13}e^{5} + \frac{16}{13}e^{4} + \frac{35}{13}e^{3} - \frac{21}{13}e^{2} - \frac{37}{13}e - \frac{7}{13}$ |
| 59 | $[59, 59, w + 43]$ | $-\frac{63}{13}e^{5} - \frac{46}{13}e^{4} - \frac{138}{13}e^{3} + \frac{75}{13}e^{2} - \frac{230}{13}e - \frac{92}{13}$ |
| 71 | $[71, 71, w + 24]$ | $\phantom{-}\frac{55}{13}e^{5} + \frac{61}{13}e^{4} + \frac{183}{13}e^{3} + \frac{15}{13}e^{2} + \frac{305}{13}e + \frac{122}{13}$ |
| 71 | $[71, 71, w + 47]$ | $-\frac{62}{13}e^{5} - \frac{30}{13}e^{4} - \frac{155}{13}e^{3} + \frac{93}{13}e^{2} - \frac{332}{13}e + \frac{31}{13}$ |
| 73 | $[73, 73, 3w - 28]$ | $\phantom{-}\frac{18}{13}e^{5} + \frac{54}{13}e^{4} + \frac{71}{13}e^{3} + \frac{90}{13}e^{2} + \frac{36}{13}e + \frac{134}{13}$ |
| 73 | $[73, 73, 12w - 107]$ | $-\frac{3}{13}e^{5} - \frac{9}{13}e^{4} - \frac{27}{13}e^{3} - \frac{15}{13}e^{2} - \frac{6}{13}e + \frac{125}{13}$ |
| 79 | $[79, 79, -w]$ | $\phantom{-}\frac{12}{13}e^{5} + \frac{36}{13}e^{4} + \frac{56}{13}e^{3} + \frac{60}{13}e^{2} + \frac{24}{13}e + \frac{124}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-\frac{6}{13}e^{5} - \frac{5}{13}e^{4} - \frac{15}{13}e^{3} + \frac{9}{13}e^{2} - \frac{25}{13}e - \frac{10}{13}$ |