Base field 3.3.1396.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 16x^{8} + x^{7} + 86x^{6} - 4x^{5} - 178x^{4} - 20x^{3} + 124x^{2} + 48x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{15}{34}e^{9} + \frac{7}{17}e^{8} - \frac{219}{34}e^{7} - \frac{169}{34}e^{6} + \frac{514}{17}e^{5} + \frac{649}{34}e^{4} - \frac{827}{17}e^{3} - \frac{447}{17}e^{2} + \frac{319}{17}e + \frac{82}{17}$ |
| 5 | $[5, 5, -w^{2} + 6]$ | $\phantom{-}\frac{1}{2}e^{8} + \frac{1}{2}e^{7} - 7e^{6} - \frac{13}{2}e^{5} + \frac{59}{2}e^{4} + 27e^{3} - 33e^{2} - 37e - 8$ |
| 5 | $[5, 5, -w + 2]$ | $-\frac{9}{34}e^{9} - \frac{5}{34}e^{8} + \frac{64}{17}e^{7} + \frac{47}{34}e^{6} - \frac{559}{34}e^{5} - \frac{57}{17}e^{4} + \frac{350}{17}e^{3} + \frac{37}{17}e^{2} - \frac{1}{17}e + \frac{46}{17}$ |
| 7 | $[7, 7, w + 2]$ | $-1$ |
| 11 | $[11, 11, 2w - 1]$ | $-\frac{11}{34}e^{9} - \frac{4}{17}e^{8} + \frac{82}{17}e^{7} + \frac{99}{34}e^{6} - \frac{386}{17}e^{5} - \frac{200}{17}e^{4} + \frac{577}{17}e^{3} + \frac{304}{17}e^{2} - \frac{124}{17}e - \frac{76}{17}$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $\phantom{-}\frac{11}{34}e^{9} - \frac{9}{34}e^{8} - \frac{181}{34}e^{7} + \frac{139}{34}e^{6} + \frac{993}{34}e^{5} - \frac{637}{34}e^{4} - \frac{1036}{17}e^{3} + \frac{376}{17}e^{2} + \frac{719}{17}e + \frac{76}{17}$ |
| 27 | $[27, 3, 3]$ | $-\frac{19}{17}e^{9} - \frac{3}{17}e^{8} + \frac{291}{17}e^{7} + \frac{18}{17}e^{6} - \frac{1454}{17}e^{5} - \frac{31}{17}e^{4} + \frac{2613}{17}e^{3} + \frac{245}{17}e^{2} - \frac{1402}{17}e - \frac{312}{17}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-\frac{2}{17}e^{9} + \frac{14}{17}e^{8} + \frac{89}{34}e^{7} - \frac{203}{17}e^{6} - \frac{332}{17}e^{5} + \frac{1791}{34}e^{4} + \frac{1015}{17}e^{3} - \frac{1098}{17}e^{2} - \frac{1147}{17}e - \frac{142}{17}$ |
| 41 | $[41, 41, 3w^{2} - w - 23]$ | $\phantom{-}\frac{11}{34}e^{9} + \frac{25}{34}e^{8} - \frac{82}{17}e^{7} - \frac{337}{34}e^{6} + \frac{823}{34}e^{5} + \frac{710}{17}e^{4} - \frac{781}{17}e^{3} - \frac{967}{17}e^{2} + \frac{379}{17}e + \frac{212}{17}$ |
| 41 | $[41, 41, w^{2} - 2]$ | $-\frac{19}{34}e^{9} + \frac{7}{17}e^{8} + \frac{291}{34}e^{7} - \frac{237}{34}e^{6} - \frac{727}{17}e^{5} + \frac{1159}{34}e^{4} + \frac{1332}{17}e^{3} - \frac{736}{17}e^{2} - \frac{837}{17}e - \frac{54}{17}$ |
| 43 | $[43, 43, w^{2} - w - 3]$ | $-\frac{15}{17}e^{9} - \frac{31}{17}e^{8} + \frac{185}{17}e^{7} + \frac{407}{17}e^{6} - \frac{586}{17}e^{5} - \frac{1652}{17}e^{4} - \frac{114}{17}e^{3} + \frac{1982}{17}e^{2} + \frac{1538}{17}e + \frac{210}{17}$ |
| 47 | $[47, 47, -w - 4]$ | $-2e^{9} - 2e^{8} + 29e^{7} + 25e^{6} - 134e^{5} - 99e^{4} + 206e^{3} + 131e^{2} - 62e - 14$ |
| 49 | $[49, 7, 3w^{2} - 2w - 24]$ | $-\frac{27}{17}e^{9} + \frac{2}{17}e^{8} + \frac{853}{34}e^{7} - \frac{63}{17}e^{6} - \frac{2238}{17}e^{5} + \frac{693}{34}e^{4} + \frac{4412}{17}e^{3} - \frac{169}{17}e^{2} - \frac{2811}{17}e - \frac{506}{17}$ |
| 53 | $[53, 53, 2w^{2} - w - 12]$ | $\phantom{-}\frac{15}{34}e^{9} - \frac{37}{34}e^{8} - \frac{253}{34}e^{7} + \frac{545}{34}e^{6} + \frac{1419}{34}e^{5} - \frac{2377}{34}e^{4} - \frac{1558}{17}e^{3} + \frac{1338}{17}e^{2} + \frac{1339}{17}e + \frac{116}{17}$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-2e^{8} - 2e^{7} + 28e^{6} + 25e^{5} - 119e^{4} - 100e^{3} + 136e^{2} + 136e + 24$ |
| 61 | $[61, 61, -w^{2} + 3w - 3]$ | $\phantom{-}\frac{1}{17}e^{9} + \frac{37}{34}e^{8} + \frac{16}{17}e^{7} - \frac{264}{17}e^{6} - \frac{671}{34}e^{5} + \frac{1163}{17}e^{4} + \frac{1524}{17}e^{3} - \frac{1457}{17}e^{2} - \frac{1951}{17}e - \frac{218}{17}$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $\phantom{-}\frac{24}{17}e^{9} + \frac{36}{17}e^{8} - \frac{313}{17}e^{7} - \frac{454}{17}e^{6} + \frac{1145}{17}e^{5} + \frac{1783}{17}e^{4} - \frac{603}{17}e^{3} - \frac{2192}{17}e^{2} - \frac{1434}{17}e - \frac{166}{17}$ |
| 79 | $[79, 79, 2w + 3]$ | $-\frac{26}{17}e^{9} - \frac{22}{17}e^{8} + \frac{366}{17}e^{7} + \frac{268}{17}e^{6} - \frac{1579}{17}e^{5} - \frac{1049}{17}e^{4} + \frac{1958}{17}e^{3} + \frac{1468}{17}e^{2} + \frac{32}{17}e - \frac{214}{17}$ |
| 89 | $[89, 89, 2w - 7]$ | $\phantom{-}\frac{49}{17}e^{9} + \frac{45}{34}e^{8} - \frac{729}{17}e^{7} - \frac{237}{17}e^{6} + \frac{6935}{34}e^{5} + \frac{802}{17}e^{4} - \frac{5598}{17}e^{3} - \frac{1285}{17}e^{2} + \frac{2287}{17}e + \frac{470}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 2]$ | $1$ |