Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[16, 4, 4]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 32x^{14} + 389x^{12} - 2252x^{10} + 6359x^{8} - 7570x^{6} + 1790x^{4} - 148x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 5]$ | $\phantom{-}\frac{8}{39}e^{15} - \frac{505}{78}e^{13} + \frac{3019}{39}e^{11} - \frac{34367}{78}e^{9} + \frac{48176}{39}e^{7} - \frac{39595}{26}e^{5} + \frac{6586}{13}e^{3} - \frac{1492}{39}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 3w - 19]$ | $\phantom{-}\frac{53}{78}e^{14} - \frac{836}{39}e^{12} + \frac{19931}{78}e^{10} - \frac{18719}{13}e^{8} + \frac{305633}{78}e^{6} - \frac{170968}{39}e^{4} + \frac{29440}{39}e^{2} - \frac{407}{13}$ |
| 11 | $[11, 11, -2w - 11]$ | $-\frac{16}{13}e^{14} + \frac{3095}{78}e^{12} - \frac{37957}{78}e^{10} + \frac{221711}{78}e^{8} - \frac{104763}{13}e^{6} + \frac{367639}{39}e^{4} - \frac{67159}{39}e^{2} + \frac{2959}{39}$ |
| 11 | $[11, 11, -2w + 13]$ | $\phantom{-}\frac{35}{78}e^{14} - \frac{375}{26}e^{12} + \frac{2291}{13}e^{10} - \frac{79961}{78}e^{8} + \frac{225941}{78}e^{6} - \frac{132203}{39}e^{4} + \frac{25175}{39}e^{2} - \frac{1135}{39}$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{47}{26}e^{15} + \frac{2254}{39}e^{13} - \frac{27350}{39}e^{11} + \frac{157696}{39}e^{9} - \frac{293967}{26}e^{7} + \frac{1018907}{78}e^{5} - \frac{94234}{39}e^{3} + \frac{4903}{39}e$ |
| 13 | $[13, 13, -w + 5]$ | $-\frac{55}{26}e^{15} + \frac{2636}{39}e^{13} - \frac{31963}{39}e^{11} + \frac{184196}{39}e^{9} - \frac{343521}{26}e^{7} + \frac{1195999}{78}e^{5} - \frac{116357}{39}e^{3} + \frac{5633}{39}e$ |
| 19 | $[19, 19, 5w - 31]$ | $-\frac{118}{39}e^{15} + \frac{1255}{13}e^{13} - \frac{15189}{13}e^{11} + \frac{261931}{39}e^{9} - \frac{730252}{39}e^{7} + \frac{842462}{39}e^{5} - \frac{158174}{39}e^{3} + \frac{7096}{39}e$ |
| 23 | $[23, 23, -w - 7]$ | $-\frac{9}{26}e^{14} + \frac{394}{39}e^{12} - \frac{4187}{39}e^{10} + \frac{39683}{78}e^{8} - \frac{13917}{13}e^{6} + \frac{30295}{39}e^{4} + \frac{1175}{39}e^{2} - \frac{482}{39}$ |
| 23 | $[23, 23, w - 8]$ | $\phantom{-}\frac{59}{39}e^{14} - \frac{621}{13}e^{12} + \frac{14825}{26}e^{10} - \frac{251089}{78}e^{8} + \frac{684817}{78}e^{6} - \frac{383791}{39}e^{4} + \frac{65281}{39}e^{2} - \frac{2768}{39}$ |
| 25 | $[25, 5, -5]$ | $-\frac{25}{26}e^{14} + \frac{1171}{39}e^{12} - \frac{27541}{78}e^{10} + \frac{76267}{39}e^{8} - \frac{135769}{26}e^{6} + \frac{224560}{39}e^{4} - \frac{41368}{39}e^{2} + \frac{1771}{39}$ |
| 31 | $[31, 31, -w - 1]$ | $\phantom{-}\frac{281}{39}e^{15} - \frac{17951}{78}e^{13} + \frac{108761}{39}e^{11} - \frac{417229}{26}e^{9} + \frac{1744442}{39}e^{7} - \frac{4003471}{78}e^{5} + \frac{351167}{39}e^{3} - \frac{5030}{13}e$ |
| 31 | $[31, 31, w - 2]$ | $-\frac{68}{39}e^{15} + \frac{2156}{39}e^{13} - \frac{25876}{39}e^{11} + \frac{147142}{39}e^{9} - \frac{404972}{39}e^{7} + \frac{153332}{13}e^{5} - \frac{27797}{13}e^{3} + \frac{3907}{39}e$ |
| 41 | $[41, 41, 6w + 31]$ | $\phantom{-}8e^{15} - \frac{766}{3}e^{13} + \frac{9272}{3}e^{11} - \frac{106541}{6}e^{9} + \frac{98751}{2}e^{7} - \frac{338231}{6}e^{5} + \frac{28522}{3}e^{3} - \frac{1168}{3}e$ |
| 41 | $[41, 41, 6w - 37]$ | $\phantom{-}\frac{139}{39}e^{15} - \frac{2973}{26}e^{13} + \frac{18115}{13}e^{11} - \frac{314884}{39}e^{9} + \frac{1768223}{78}e^{7} - \frac{1020590}{39}e^{5} + \frac{176021}{39}e^{3} - \frac{6469}{39}e$ |
| 43 | $[43, 43, -3w - 17]$ | $\phantom{-}\frac{15}{13}e^{14} - \frac{471}{13}e^{12} + \frac{5581}{13}e^{10} - \frac{31227}{13}e^{8} + \frac{84441}{13}e^{6} - \frac{94530}{13}e^{4} + \frac{17881}{13}e^{2} - \frac{919}{13}$ |
| 43 | $[43, 43, -3w + 20]$ | $\phantom{-}\frac{5}{26}e^{14} - \frac{242}{39}e^{12} + \frac{5945}{78}e^{10} - \frac{17414}{39}e^{8} + \frac{33113}{26}e^{6} - \frac{59030}{39}e^{4} + \frac{12197}{39}e^{2} - \frac{635}{39}$ |
| 59 | $[59, 59, 3w - 17]$ | $-\frac{77}{39}e^{15} + \frac{825}{13}e^{13} - \frac{10083}{13}e^{11} + \frac{176117}{39}e^{9} - \frac{498950}{39}e^{7} + \frac{589072}{39}e^{5} - \frac{121378}{39}e^{3} + \frac{5228}{39}e$ |
| 59 | $[59, 59, 3w + 14]$ | $-\frac{74}{39}e^{15} + \frac{2347}{39}e^{13} - \frac{28163}{39}e^{11} + \frac{53282}{13}e^{9} - \frac{436736}{39}e^{7} + \frac{482078}{39}e^{5} - \frac{61322}{39}e^{3} + \frac{176}{13}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |