Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + 2w + 6]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - x^{8} - 12x^{7} + 10x^{6} + 44x^{5} - 26x^{4} - 57x^{3} + 18x^{2} + 22x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{3}{17}e^{8} + \frac{6}{17}e^{7} - \frac{35}{17}e^{6} - \frac{75}{17}e^{5} + \frac{111}{17}e^{4} + 16e^{3} - \frac{69}{17}e^{2} - 15e - \frac{36}{17}$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $\phantom{-}\frac{5}{17}e^{8} - \frac{7}{17}e^{7} - \frac{64}{17}e^{6} + \frac{79}{17}e^{5} + \frac{253}{17}e^{4} - 15e^{3} - \frac{336}{17}e^{2} + 14e + \frac{110}{17}$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $-\frac{6}{17}e^{8} + \frac{5}{17}e^{7} + \frac{70}{17}e^{6} - \frac{54}{17}e^{5} - \frac{239}{17}e^{4} + 10e^{3} + \frac{240}{17}e^{2} - 10e - \frac{30}{17}$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $-1$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $\phantom{-}\frac{10}{17}e^{8} - \frac{14}{17}e^{7} - \frac{111}{17}e^{6} + \frac{141}{17}e^{5} + \frac{353}{17}e^{4} - 22e^{3} - \frac{366}{17}e^{2} + 16e + \frac{84}{17}$ |
| 19 | $[19, 19, -w + 2]$ | $\phantom{-}\frac{4}{17}e^{8} - \frac{9}{17}e^{7} - \frac{41}{17}e^{6} + \frac{87}{17}e^{5} + \frac{97}{17}e^{4} - 12e^{3} + \frac{10}{17}e^{2} + 6e - \frac{82}{17}$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $-\frac{12}{17}e^{8} + \frac{10}{17}e^{7} + \frac{140}{17}e^{6} - \frac{91}{17}e^{5} - \frac{461}{17}e^{4} + 11e^{3} + \frac{361}{17}e^{2} - 4e + \frac{76}{17}$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $-\frac{5}{17}e^{8} - \frac{10}{17}e^{7} + \frac{64}{17}e^{6} + \frac{125}{17}e^{5} - \frac{253}{17}e^{4} - 26e^{3} + \frac{336}{17}e^{2} + 21e - \frac{110}{17}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{19}{17}e^{8} + \frac{4}{17}e^{7} - \frac{233}{17}e^{6} - \frac{67}{17}e^{5} + \frac{839}{17}e^{4} + 17e^{3} - \frac{845}{17}e^{2} - 14e + \frac{44}{17}$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $-\frac{6}{17}e^{8} + \frac{5}{17}e^{7} + \frac{70}{17}e^{6} - \frac{37}{17}e^{5} - \frac{239}{17}e^{4} + 2e^{3} + \frac{257}{17}e^{2} + e - \frac{132}{17}$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $-\frac{10}{17}e^{8} + \frac{14}{17}e^{7} + \frac{111}{17}e^{6} - \frac{124}{17}e^{5} - \frac{353}{17}e^{4} + 13e^{3} + \frac{366}{17}e^{2} - e - \frac{118}{17}$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $-\frac{6}{17}e^{8} - \frac{12}{17}e^{7} + \frac{87}{17}e^{6} + \frac{133}{17}e^{5} - \frac{375}{17}e^{4} - 24e^{3} + \frac{427}{17}e^{2} + 18e + \frac{4}{17}$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $-\frac{25}{17}e^{8} + \frac{18}{17}e^{7} + \frac{286}{17}e^{6} - \frac{157}{17}e^{5} - \frac{942}{17}e^{4} + 18e^{3} + \frac{932}{17}e^{2} - 12e - \frac{176}{17}$ |
| 47 | $[47, 47, -2w + 7]$ | $\phantom{-}\frac{16}{17}e^{8} - \frac{19}{17}e^{7} - \frac{181}{17}e^{6} + \frac{178}{17}e^{5} + \frac{592}{17}e^{4} - 23e^{3} - \frac{606}{17}e^{2} + 12e + \frac{80}{17}$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $-\frac{36}{17}e^{8} + \frac{30}{17}e^{7} + \frac{420}{17}e^{6} - \frac{290}{17}e^{5} - \frac{1417}{17}e^{4} + 41e^{3} + \frac{1389}{17}e^{2} - 25e - \frac{214}{17}$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}\frac{14}{17}e^{8} - \frac{6}{17}e^{7} - \frac{152}{17}e^{6} + \frac{41}{17}e^{5} + \frac{416}{17}e^{4} - e^{3} - \frac{118}{17}e^{2} - 4e - \frac{168}{17}$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $\phantom{-}\frac{25}{17}e^{8} - \frac{18}{17}e^{7} - \frac{303}{17}e^{6} + \frac{174}{17}e^{5} + \frac{1112}{17}e^{4} - 25e^{3} - \frac{1306}{17}e^{2} + 18e + \frac{244}{17}$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $-\frac{19}{17}e^{8} + \frac{13}{17}e^{7} + \frac{233}{17}e^{6} - \frac{120}{17}e^{5} - \frac{856}{17}e^{4} + 14e^{3} + \frac{981}{17}e^{2} - 4e - \frac{214}{17}$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{11}{17}e^{8} + \frac{5}{17}e^{7} - \frac{117}{17}e^{6} - \frac{71}{17}e^{5} + \frac{305}{17}e^{4} + 17e^{3} - \frac{32}{17}e^{2} - 13e - \frac{268}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + 2w + 6]$ | $1$ |