Base field 3.3.1765.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 11x + 16\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[16, 4, w^{2} + 3w - 7]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 22x^{14} + 193x^{12} - 861x^{10} + 2055x^{8} - 2506x^{6} + 1340x^{4} - 256x^{2} + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} - w + 9]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -2w^{2} - w + 21]$ | $\phantom{-}\frac{43}{263}e^{14} - \frac{861}{263}e^{12} + \frac{6701}{263}e^{10} - \frac{25679}{263}e^{8} + \frac{50534}{263}e^{6} - \frac{47725}{263}e^{4} + \frac{16675}{263}e^{2} - \frac{780}{263}$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{93}{263}e^{14} - \frac{1801}{263}e^{12} + \frac{13343}{263}e^{10} - \frac{47422}{263}e^{8} + \frac{82707}{263}e^{6} - \frac{63286}{263}e^{4} + \frac{14260}{263}e^{2} + \frac{258}{263}$ |
| 13 | $[13, 13, -2w^{2} - w + 19]$ | $\phantom{-}\frac{126}{263}e^{15} - \frac{2474}{263}e^{13} + \frac{18663}{263}e^{11} - \frac{67753}{263}e^{9} + \frac{119758}{263}e^{7} - \frac{85649}{263}e^{5} + \frac{2225}{263}e^{3} + \frac{9843}{263}e$ |
| 13 | $[13, 13, w^{2} - 9]$ | $-\frac{104}{263}e^{14} + \frac{2113}{263}e^{12} - \frac{16782}{263}e^{10} + \frac{66034}{263}e^{8} - \frac{133543}{263}e^{6} + \frac{126058}{263}e^{4} - \frac{37425}{263}e^{2} + \frac{755}{263}$ |
| 13 | $[13, 13, 3w^{2} + 2w - 29]$ | $\phantom{-}\frac{38}{263}e^{15} - \frac{767}{263}e^{13} + \frac{6142}{263}e^{11} - \frac{25372}{263}e^{9} + \frac{59441}{263}e^{7} - \frac{81069}{263}e^{5} + \frac{58865}{263}e^{3} - \frac{14139}{263}e$ |
| 17 | $[17, 17, -w^{2} - 2w + 7]$ | $-\frac{42}{263}e^{15} + \frac{1000}{263}e^{13} - \frac{9377}{263}e^{11} + \frac{43449}{263}e^{9} - \frac{101023}{263}e^{7} + \frac{101313}{263}e^{5} - \frac{18801}{263}e^{3} - \frac{6437}{263}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{216}{263}e^{15} + \frac{4429}{263}e^{13} - \frac{35563}{263}e^{11} + \frac{141922}{263}e^{9} - \frac{293968}{263}e^{7} + \frac{296286}{263}e^{5} - \frac{117280}{263}e^{3} + \frac{12958}{263}e$ |
| 27 | $[27, 3, -3]$ | $-\frac{68}{263}e^{14} + \frac{1331}{263}e^{12} - \frac{10022}{263}e^{10} + \frac{36682}{263}e^{8} - \frac{68330}{263}e^{6} + \frac{62475}{263}e^{4} - \frac{24541}{263}e^{2} + \frac{1313}{263}$ |
| 31 | $[31, 31, -w^{2} + 7]$ | $\phantom{-}\frac{27}{263}e^{15} - \frac{455}{263}e^{13} + \frac{2703}{263}e^{11} - \frac{6760}{263}e^{9} + \frac{8605}{263}e^{7} - \frac{18297}{263}e^{5} + \frac{35437}{263}e^{3} - \frac{11548}{263}e$ |
| 43 | $[43, 43, w^{2} - 13]$ | $-\frac{30}{263}e^{14} + \frac{301}{263}e^{12} + \frac{854}{263}e^{10} - \frac{19987}{263}e^{8} + \frac{82372}{263}e^{6} - \frac{123794}{263}e^{4} + \frac{51156}{263}e^{2} - \frac{3358}{263}$ |
| 47 | $[47, 47, 2w^{2} + 3w - 11]$ | $-\frac{37}{263}e^{15} + \frac{643}{263}e^{13} - \frac{4084}{263}e^{11} + \frac{11845}{263}e^{9} - \frac{18143}{263}e^{7} + \frac{23934}{263}e^{5} - \frac{28379}{263}e^{3} + \frac{6396}{263}e$ |
| 59 | $[59, 59, w^{2} - 5]$ | $-\frac{102}{263}e^{15} + \frac{1865}{263}e^{13} - \frac{12666}{263}e^{11} + \frac{39243}{263}e^{9} - \frac{54892}{263}e^{7} + \frac{31513}{263}e^{5} - \frac{12484}{263}e^{3} + \frac{1838}{263}e$ |
| 61 | $[61, 61, 5w^{2} + 4w - 47]$ | $-\frac{2}{263}e^{15} - \frac{15}{263}e^{13} + \frac{618}{263}e^{11} - \frac{4243}{263}e^{9} + \frac{9454}{263}e^{7} + \frac{1180}{263}e^{5} - \frac{23100}{263}e^{3} + \frac{11541}{263}e$ |
| 61 | $[61, 61, 4w - 7]$ | $\phantom{-}\frac{194}{263}e^{15} - \frac{4068}{263}e^{13} + \frac{33419}{263}e^{11} - \frac{135732}{263}e^{9} + \frac{280138}{263}e^{7} - \frac{261477}{263}e^{5} + \frac{65953}{263}e^{3} + \frac{6163}{263}e$ |
| 61 | $[61, 61, w - 5]$ | $-\frac{37}{263}e^{14} + \frac{643}{263}e^{12} - \frac{4084}{263}e^{10} + \frac{11582}{263}e^{8} - \frac{14461}{263}e^{6} + \frac{6839}{263}e^{4} - \frac{238}{263}e^{2} - \frac{2020}{263}$ |
| 71 | $[71, 71, -2w^{2} - 2w + 21]$ | $\phantom{-}\frac{56}{263}e^{15} - \frac{1158}{263}e^{13} + \frac{9259}{263}e^{11} - \frac{35577}{263}e^{9} + \frac{64564}{263}e^{7} - \frac{39352}{263}e^{5} - \frac{14119}{263}e^{3} + \frac{7180}{263}e$ |
| 73 | $[73, 73, -2w^{2} + 4w - 1]$ | $\phantom{-}\frac{193}{263}e^{15} - \frac{4470}{263}e^{13} + \frac{41092}{263}e^{11} - \frac{189270}{263}e^{9} + \frac{450029}{263}e^{7} - \frac{500743}{263}e^{5} + \frac{184588}{263}e^{3} - \frac{12131}{263}e$ |
| 79 | $[79, 79, w + 5]$ | $-\frac{52}{263}e^{14} + \frac{925}{263}e^{12} - \frac{6024}{263}e^{10} + \frac{17500}{263}e^{8} - \frac{22456}{263}e^{6} + \frac{13585}{263}e^{4} - \frac{9376}{263}e^{2} - \frac{1069}{263}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{2} - w + 9]$ | $1$ |