Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 67x^{12} + 1667x^{10} - 18938x^{8} + 98600x^{6} - 219244x^{4} + 182016x^{2} - 27648\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}\frac{27331}{52633024}e^{12} - \frac{1497593}{52633024}e^{10} + \frac{89422411}{157899072}e^{8} - \frac{132111167}{26316512}e^{6} + \frac{378927569}{19737384}e^{4} - \frac{1001940499}{39474768}e^{2} + \frac{5887509}{822391}$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 2]$ | $-\frac{270589}{947394432}e^{13} + \frac{16515487}{947394432}e^{11} - \frac{370682351}{947394432}e^{9} + \frac{1857743749}{473697216}e^{7} - \frac{1998379291}{118424304}e^{5} + \frac{6128752927}{236848608}e^{3} - \frac{32937091}{3289564}e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{1669}{947394432}e^{13} + \frac{1116001}{947394432}e^{11} - \frac{53316929}{947394432}e^{9} + \frac{136930877}{157899072}e^{7} - \frac{620862107}{118424304}e^{5} + \frac{944261395}{78949536}e^{3} - \frac{9996005}{1644782}e$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $-\frac{3735}{13158256}e^{13} + \frac{137746}{7401519}e^{11} - \frac{26499955}{59212152}e^{9} + \frac{567134095}{118424304}e^{7} - \frac{145513411}{6579128}e^{5} + \frac{1120192139}{29606076}e^{3} - \frac{56218665}{3289564}e$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $\phantom{-}\frac{81917}{210532096}e^{13} - \frac{45638495}{1894788864}e^{11} + \frac{1040259199}{1894788864}e^{9} - \frac{5309150329}{947394432}e^{7} + \frac{652850301}{26316512}e^{5} - \frac{19310290759}{473697216}e^{3} + \frac{72294069}{3289564}e$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{538043}{1894788864}e^{13} + \frac{9456907}{631596288}e^{11} - \frac{177742955}{631596288}e^{9} + \frac{2146345879}{947394432}e^{7} - \frac{1632867203}{236848608}e^{5} + \frac{821701273}{473697216}e^{3} + \frac{24653771}{3289564}e$ |
| 23 | $[23, 23, -w + 4]$ | $\phantom{-}\frac{8539}{78949536}e^{12} - \frac{408193}{78949536}e^{10} + \frac{7286177}{78949536}e^{8} - \frac{34899655}{39474768}e^{6} + \frac{52180927}{9868692}e^{4} - \frac{270930913}{19737384}e^{2} + \frac{2850306}{822391}$ |
| 27 | $[27, 3, 3]$ | $-\frac{149441}{236848608}e^{12} + \frac{7405747}{236848608}e^{10} - \frac{129333683}{236848608}e^{8} + \frac{54866989}{13158256}e^{6} - \frac{414503081}{29606076}e^{4} + \frac{299770465}{19737384}e^{2} + \frac{2902972}{822391}$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $\phantom{-}\frac{214237}{473697216}e^{12} - \frac{7408967}{473697216}e^{10} + \frac{47042983}{473697216}e^{8} + \frac{25196919}{26316512}e^{6} - \frac{458159867}{59212152}e^{4} + \frac{175158971}{39474768}e^{2} + \frac{7153827}{822391}$ |
| 31 | $[31, 31, w^{2} - 10]$ | $-\frac{8539}{78949536}e^{12} + \frac{408193}{78949536}e^{10} - \frac{7286177}{78949536}e^{8} + \frac{34899655}{39474768}e^{6} - \frac{52180927}{9868692}e^{4} + \frac{290668297}{19737384}e^{2} - \frac{9429434}{822391}$ |
| 41 | $[41, 41, w + 4]$ | $\phantom{-}\frac{240491}{473697216}e^{12} - \frac{15137569}{473697216}e^{10} + \frac{348905825}{473697216}e^{8} - \frac{196977815}{26316512}e^{6} + \frac{1859058023}{59212152}e^{4} - \frac{1565209123}{39474768}e^{2} + \frac{6345066}{822391}$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}\frac{6473}{1894788864}e^{13} - \frac{809417}{631596288}e^{11} + \frac{33833993}{631596288}e^{9} - \frac{747556357}{947394432}e^{7} + \frac{1122167165}{236848608}e^{5} - \frac{5770236211}{473697216}e^{3} + \frac{11044495}{822391}e$ |
| 41 | $[41, 41, -2w - 5]$ | $-\frac{1075883}{1894788864}e^{13} + \frac{63633697}{1894788864}e^{11} - \frac{1381227425}{1894788864}e^{9} + \frac{742602071}{105266048}e^{7} - \frac{6871349999}{236848608}e^{5} + \frac{2082752833}{52633024}e^{3} - \frac{15782447}{1644782}e$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{123883}{1894788864}e^{13} + \frac{8002321}{1894788864}e^{11} - \frac{171231857}{1894788864}e^{9} + \frac{610705495}{947394432}e^{7} + \frac{137087909}{236848608}e^{5} - \frac{7172525015}{473697216}e^{3} + \frac{63158113}{3289564}e$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}\frac{99605}{947394432}e^{13} - \frac{8633887}{947394432}e^{11} + \frac{253515167}{947394432}e^{9} - \frac{527134075}{157899072}e^{7} + \frac{2121392753}{118424304}e^{5} - \frac{3081431581}{78949536}e^{3} + \frac{24236960}{822391}e$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $\phantom{-}\frac{961811}{1894788864}e^{13} - \frac{55827625}{1894788864}e^{11} + \frac{1204863689}{1894788864}e^{9} - \frac{666520471}{105266048}e^{7} + \frac{6888880859}{236848608}e^{5} - \frac{2891329817}{52633024}e^{3} + \frac{115619413}{3289564}e$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $\phantom{-}\frac{209377}{1894788864}e^{13} - \frac{15294419}{1894788864}e^{11} + \frac{377888371}{1894788864}e^{9} - \frac{596855255}{315798144}e^{7} + \frac{1064964097}{236848608}e^{5} + \frac{691252413}{52633024}e^{3} - \frac{102610799}{3289564}e$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{68911}{210532096}e^{13} - \frac{12631607}{631596288}e^{11} + \frac{94057693}{210532096}e^{9} - \frac{1382597137}{315798144}e^{7} + \frac{1358881141}{78949536}e^{5} - \frac{826502549}{52633024}e^{3} - \frac{44114447}{3289564}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, 2]$ | $-1$ |