Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} + w + 6]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 80x^{12} + 2604x^{10} - 44113x^{8} + 411093x^{6} - 2025532x^{4} + 4443648x^{2} - 2146304\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $-\frac{2534629}{11465804800}e^{12} + \frac{10375869}{716612800}e^{10} - \frac{42097135}{114658048}e^{8} + \frac{51821039477}{11465804800}e^{6} - \frac{314912646089}{11465804800}e^{4} + \frac{205367130043}{2866451200}e^{2} - \frac{1795076809}{44788300}$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{87917}{5732902400}e^{12} + \frac{533037}{358306400}e^{10} - \frac{3225351}{57329024}e^{8} + \frac{5846673021}{5732902400}e^{6} - \frac{49997040497}{5732902400}e^{4} + \frac{40609766739}{1433225600}e^{2} - \frac{248790457}{22394150}$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 1]$ | $-\frac{2108017}{5732902400}e^{12} + \frac{8277177}{358306400}e^{10} - \frac{159346399}{286645120}e^{8} + \frac{36678161601}{5732902400}e^{6} - \frac{204283715397}{5732902400}e^{4} + \frac{119456559599}{1433225600}e^{2} - \frac{911758517}{22394150}$ |
| 8 | $[8, 2, 2]$ | $-\frac{6769839}{45863219200}e^{13} + \frac{27078479}{2866451200}e^{11} - \frac{105697485}{458632192}e^{9} + \frac{122056551007}{45863219200}e^{7} - \frac{668342663899}{45863219200}e^{5} + \frac{369191332113}{11465804800}e^{3} - \frac{2273766369}{179153200}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{13767711}{11465804800}e^{12} + \frac{56763591}{716612800}e^{10} - \frac{1158697617}{573290240}e^{8} + \frac{285998271183}{11465804800}e^{6} - \frac{1727007213451}{11465804800}e^{4} + \frac{1096322596417}{2866451200}e^{2} - \frac{8658485511}{44788300}$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}\frac{1678}{11197075}e^{13} - \frac{110408}{11197075}e^{11} + \frac{1128579}{4478830}e^{9} - \frac{35084049}{11197075}e^{7} + \frac{215297323}{11197075}e^{5} - \frac{1131823693}{22394150}e^{3} + \frac{710492321}{22394150}e$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{3805029}{45863219200}e^{13} + \frac{16326189}{2866451200}e^{11} - \frac{349008427}{2293160960}e^{9} + \frac{90407459317}{45863219200}e^{7} - \frac{567350710089}{45863219200}e^{5} + \frac{356073609723}{11465804800}e^{3} - \frac{1572664489}{179153200}e$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{13693977}{45863219200}e^{13} - \frac{54988337}{2866451200}e^{11} + \frac{1086195639}{2293160960}e^{9} - \frac{257216706281}{45863219200}e^{7} + \frac{1473387865357}{45863219200}e^{5} - \frac{876534160519}{11465804800}e^{3} + \frac{6366067977}{179153200}e$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-\frac{336281}{2293160960}e^{12} + \frac{1235697}{143322560}e^{10} - \frac{108207123}{573290240}e^{8} + \frac{861411349}{458632192}e^{6} - \frac{18730956941}{2293160960}e^{4} + \frac{6709197831}{573290240}e^{2} + \frac{4236987}{1791532}$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $-\frac{6820889}{45863219200}e^{13} + \frac{26723889}{2866451200}e^{11} - \frac{508363191}{2293160960}e^{9} + \frac{113512441577}{45863219200}e^{7} - \frac{591530030349}{45863219200}e^{5} + \frac{297040429703}{11465804800}e^{3} - \frac{682129409}{179153200}e$ |
| 37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{17356441}{91726438400}e^{13} - \frac{74619201}{5732902400}e^{11} + \frac{320013067}{917264384}e^{9} - \frac{418834640233}{91726438400}e^{7} + \frac{2712032739981}{91726438400}e^{5} - \frac{1864826693447}{22931609600}e^{3} + \frac{16715284061}{358306400}e$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{5184017}{2866451200}e^{12} + \frac{21759497}{179153200}e^{10} - \frac{453016191}{143322560}e^{8} + \frac{114268460641}{2866451200}e^{6} - \frac{706443984997}{2866451200}e^{4} + \frac{458951587279}{716612800}e^{2} - \frac{3660515697}{11197075}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{6945673}{22931609600}e^{13} - \frac{28144553}{1433225600}e^{11} + \frac{112148187}{229316096}e^{9} - \frac{133749897049}{22931609600}e^{7} + \frac{768336744893}{22931609600}e^{5} - \frac{447544414391}{5732902400}e^{3} + \frac{2233887683}{89576600}e$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $-\frac{23863829}{91726438400}e^{13} + \frac{92825149}{5732902400}e^{11} - \frac{1740121723}{4586321920}e^{9} + \frac{377366268837}{91726438400}e^{7} - \frac{1851624834489}{91726438400}e^{5} + \frac{808035433163}{22931609600}e^{3} + \frac{407233071}{358306400}e$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{9354913}{5732902400}e^{12} - \frac{38004113}{358306400}e^{10} + \frac{761783727}{286645120}e^{8} - \frac{183846170609}{5732902400}e^{6} + \frac{1080798417333}{5732902400}e^{4} - \frac{669197958751}{1433225600}e^{2} + \frac{5470868753}{22394150}$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $-\frac{4139459}{11465804800}e^{13} + \frac{17086239}{716612800}e^{11} - \frac{348879149}{573290240}e^{9} + \frac{86172487347}{11465804800}e^{7} - \frac{523786381119}{11465804800}e^{5} + \frac{344273021613}{2866451200}e^{3} - \frac{1702391537}{22394150}e$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $\phantom{-}\frac{3432711}{1433225600}e^{12} - \frac{13968991}{89576600}e^{10} + \frac{280611657}{71661280}e^{8} - \frac{67901872183}{1433225600}e^{6} + \frac{400049384851}{1433225600}e^{4} - \frac{246607094617}{358306400}e^{2} + \frac{3778532522}{11197075}$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $-\frac{17832109}{91726438400}e^{13} + \frac{72029749}{5732902400}e^{11} - \frac{284282439}{917264384}e^{9} + \frac{331156304317}{91726438400}e^{7} - \frac{1803266193969}{91726438400}e^{5} + \frac{926101793203}{22931609600}e^{3} - \frac{1015530689}{358306400}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 2]$ | $-1$ |