Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w + 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + x^{11} - 19x^{10} - 18x^{9} + 132x^{8} + 120x^{7} - 403x^{6} - 350x^{5} + 498x^{4} + 399x^{3} - 162x^{2} - 120x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $-\frac{3}{76}e^{11} - \frac{5}{76}e^{10} + \frac{15}{19}e^{9} + \frac{75}{76}e^{8} - \frac{115}{19}e^{7} - \frac{369}{76}e^{6} + \frac{1609}{76}e^{5} + \frac{571}{76}e^{4} - \frac{2285}{76}e^{3} + \frac{87}{38}e^{2} + \frac{659}{76}e - \frac{107}{38}$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{17}{76}e^{11} + \frac{4}{19}e^{10} + \frac{321}{76}e^{9} - \frac{259}{76}e^{8} - \frac{2157}{76}e^{7} + \frac{1367}{76}e^{6} + \frac{3099}{38}e^{5} - \frac{662}{19}e^{4} - \frac{1763}{19}e^{3} + \frac{1537}{76}e^{2} + \frac{2227}{76}e - \frac{117}{76}$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $\phantom{-}\frac{4}{19}e^{11} - \frac{43}{76}e^{10} - \frac{263}{76}e^{9} + \frac{351}{38}e^{8} + \frac{1383}{76}e^{7} - \frac{1885}{38}e^{6} - \frac{2381}{76}e^{5} + \frac{7411}{76}e^{4} + \frac{185}{76}e^{3} - \frac{3835}{76}e^{2} + \frac{65}{19}e + \frac{375}{76}$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{10}{19}e^{11} - \frac{41}{76}e^{10} - \frac{705}{76}e^{9} + \frac{168}{19}e^{8} + \frac{4303}{76}e^{7} - \frac{879}{19}e^{6} - \frac{10655}{76}e^{5} + \frac{6339}{76}e^{4} + \frac{9269}{76}e^{3} - \frac{2301}{76}e^{2} - \frac{455}{19}e + \frac{111}{76}$ |
| 13 | $[13, 13, -2w + 1]$ | $-\frac{2}{19}e^{11} - \frac{7}{76}e^{10} + \frac{141}{76}e^{9} + \frac{31}{19}e^{8} - \frac{891}{76}e^{7} - \frac{208}{19}e^{6} + \frac{2435}{76}e^{5} + \frac{2441}{76}e^{4} - \frac{2705}{76}e^{3} - \frac{2595}{76}e^{2} + \frac{205}{19}e + \frac{373}{76}$ |
| 19 | $[19, 19, 2w^{2} - w - 15]$ | $\phantom{-}\frac{9}{76}e^{11} + \frac{15}{76}e^{10} - \frac{45}{19}e^{9} - \frac{225}{76}e^{8} + \frac{345}{19}e^{7} + \frac{1107}{76}e^{6} - \frac{4903}{76}e^{5} - \frac{1865}{76}e^{4} + \frac{7463}{76}e^{3} + \frac{233}{38}e^{2} - \frac{2889}{76}e - \frac{21}{38}$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{17}{76}e^{11} - \frac{35}{76}e^{10} - \frac{66}{19}e^{9} + \frac{601}{76}e^{8} + \frac{316}{19}e^{7} - \frac{3381}{76}e^{6} - \frac{1619}{76}e^{5} + \frac{6923}{76}e^{4} - \frac{1251}{76}e^{3} - \frac{902}{19}e^{2} + \frac{965}{76}e + \frac{91}{19}$ |
| 27 | $[27, 3, 3]$ | $-\frac{12}{19}e^{11} + \frac{17}{38}e^{10} + \frac{423}{38}e^{9} - \frac{137}{19}e^{8} - \frac{2597}{38}e^{7} + \frac{671}{19}e^{6} + \frac{6545}{38}e^{5} - \frac{1949}{38}e^{4} - \frac{6025}{38}e^{3} - \frac{185}{38}e^{2} + \frac{793}{19}e + \frac{321}{38}$ |
| 31 | $[31, 31, w^{2} - 2w - 1]$ | $-\frac{35}{38}e^{11} + \frac{12}{19}e^{10} + \frac{605}{38}e^{9} - \frac{417}{38}e^{8} - \frac{3625}{38}e^{7} + \frac{2269}{38}e^{6} + \frac{4411}{19}e^{5} - \frac{2081}{19}e^{4} - \frac{3845}{19}e^{3} + \frac{1327}{38}e^{2} + \frac{1887}{38}e + \frac{119}{38}$ |
| 37 | $[37, 37, -3w^{2} + 2w + 23]$ | $\phantom{-}\frac{23}{76}e^{11} - \frac{25}{76}e^{10} - \frac{96}{19}e^{9} + \frac{451}{76}e^{8} + \frac{546}{19}e^{7} - \frac{2643}{76}e^{6} - \frac{4837}{76}e^{5} + \frac{5705}{76}e^{4} + \frac{3319}{76}e^{3} - \frac{837}{19}e^{2} - \frac{353}{76}e + \frac{65}{19}$ |
| 41 | $[41, 41, -2w - 1]$ | $\phantom{-}\frac{21}{76}e^{11} - \frac{3}{76}e^{10} - \frac{105}{19}e^{9} + \frac{45}{76}e^{8} + \frac{767}{19}e^{7} - \frac{229}{76}e^{6} - \frac{9895}{76}e^{5} + \frac{639}{76}e^{4} + \frac{12993}{76}e^{3} - \frac{314}{19}e^{2} - \frac{4271}{76}e + \frac{137}{19}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{20}{19}e^{11} + \frac{11}{19}e^{10} + \frac{362}{19}e^{9} - \frac{184}{19}e^{8} - \frac{2332}{19}e^{7} + \frac{941}{19}e^{6} + \frac{6420}{19}e^{5} - \frac{1507}{19}e^{4} - \frac{7019}{19}e^{3} + \frac{153}{19}e^{2} + \frac{2221}{19}e + \frac{182}{19}$ |
| 49 | $[49, 7, w^{2} - 2w - 5]$ | $-\frac{13}{38}e^{11} + \frac{39}{76}e^{10} + \frac{425}{76}e^{9} - \frac{170}{19}e^{8} - \frac{2321}{76}e^{7} + \frac{977}{19}e^{6} + \frac{4793}{76}e^{5} - \frac{8383}{76}e^{4} - \frac{2925}{76}e^{3} + \frac{4985}{76}e^{2} + \frac{183}{38}e - \frac{341}{76}$ |
| 59 | $[59, 59, 2w - 3]$ | $-\frac{6}{19}e^{11} - \frac{1}{38}e^{10} + \frac{221}{38}e^{9} + \frac{17}{19}e^{8} - \frac{1441}{38}e^{7} - \frac{187}{19}e^{6} + \frac{3947}{38}e^{5} + \frac{1505}{38}e^{4} - \frac{4067}{38}e^{3} - \frac{1907}{38}e^{2} + \frac{482}{19}e + \frac{455}{38}$ |
| 67 | $[67, 67, w - 5]$ | $-\frac{3}{2}e^{11} + e^{10} + \frac{53}{2}e^{9} - \frac{35}{2}e^{8} - \frac{329}{2}e^{7} + \frac{195}{2}e^{6} + 427e^{5} - 193e^{4} - 427e^{3} + \frac{191}{2}e^{2} + \frac{263}{2}e - \frac{7}{2}$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $-\frac{7}{19}e^{11} + \frac{23}{76}e^{10} + \frac{503}{76}e^{9} - \frac{201}{38}e^{8} - \frac{3223}{76}e^{7} + \frac{1109}{38}e^{6} + \frac{8893}{76}e^{5} - \frac{4139}{76}e^{4} - \frac{10085}{76}e^{3} + \frac{1187}{76}e^{2} + \frac{993}{19}e + \frac{593}{76}$ |
| 73 | $[73, 73, w^{2} + 1]$ | $\phantom{-}\frac{39}{38}e^{11} - \frac{15}{19}e^{10} - \frac{685}{38}e^{9} + \frac{507}{38}e^{8} + \frac{4213}{38}e^{7} - \frac{2689}{38}e^{6} - \frac{5376}{19}e^{5} + \frac{2397}{19}e^{4} + \frac{5096}{19}e^{3} - \frac{1445}{38}e^{2} - \frac{2335}{38}e - \frac{125}{38}$ |
| 83 | $[83, 83, -4w^{2} + 3w + 27]$ | $\phantom{-}\frac{1}{19}e^{11} - \frac{11}{19}e^{10} - \frac{20}{19}e^{9} + \frac{165}{19}e^{8} + \frac{109}{19}e^{7} - \frac{808}{19}e^{6} - \frac{131}{19}e^{5} + \frac{1374}{19}e^{4} - \frac{182}{19}e^{3} - \frac{400}{19}e^{2} + \frac{21}{19}e - \frac{144}{19}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 1]$ | $-1$ |