Base field \(\Q(\sqrt{185}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 46\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,8,-w + 3]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} + 31x^{16} + 395x^{14} + 2674x^{12} + 10403x^{10} + 23623x^{8} + 30729x^{6} + 21872x^{4} + 7680x^{2} + 1024\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{69}{224}e^{17} - \frac{2057}{224}e^{15} - \frac{24821}{224}e^{13} - \frac{38819}{56}e^{11} - \frac{535943}{224}e^{9} - \frac{1006409}{224}e^{7} - \frac{959719}{224}e^{5} - \frac{29835}{16}e^{3} - \frac{2063}{7}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{3}{56}e^{16} + \frac{87}{56}e^{14} + \frac{1011}{56}e^{12} + \frac{2993}{28}e^{10} + \frac{18915}{56}e^{8} + \frac{30239}{56}e^{6} + \frac{20271}{56}e^{4} + 53e^{2} - \frac{81}{7}$ |
| 11 | $[11, 11, 2w + 13]$ | $\phantom{-}e^{2} + 3$ |
| 11 | $[11, 11, -2w + 15]$ | $\phantom{-}\frac{101}{112}e^{16} + \frac{3013}{112}e^{14} + \frac{36375}{112}e^{12} + \frac{28449}{14}e^{10} + \frac{785121}{112}e^{8} + \frac{1471315}{112}e^{6} + \frac{1395267}{112}e^{4} + 5347e^{2} + \frac{5731}{7}$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{53}{448}e^{17} + \frac{1579}{448}e^{15} + \frac{19023}{448}e^{13} + \frac{59293}{224}e^{11} + \frac{406167}{448}e^{9} + \frac{749659}{448}e^{7} + \frac{686589}{448}e^{5} + \frac{4875}{8}e^{3} + \frac{585}{7}e$ |
| 13 | $[13, 13, w + 8]$ | $\phantom{-}\frac{27}{56}e^{17} + \frac{201}{14}e^{15} + \frac{1210}{7}e^{13} + \frac{60307}{56}e^{11} + \frac{206565}{56}e^{9} + \frac{47780}{7}e^{7} + \frac{88483}{14}e^{5} + \frac{20787}{8}e^{3} + \frac{2617}{7}e$ |
| 17 | $[17, 17, w + 3]$ | $-\frac{3}{8}e^{17} - \frac{179}{16}e^{15} - \frac{2161}{16}e^{13} - \frac{13519}{16}e^{11} - \frac{11653}{4}e^{9} - \frac{87213}{16}e^{7} - \frac{82309}{16}e^{5} - \frac{34801}{16}e^{3} - 317e$ |
| 17 | $[17, 17, w + 13]$ | $-\frac{201}{448}e^{17} - \frac{6011}{448}e^{15} - \frac{72847}{448}e^{13} - \frac{229287}{224}e^{11} - \frac{1597971}{448}e^{9} - \frac{3047803}{448}e^{7} - \frac{2985293}{448}e^{5} - \frac{48455}{16}e^{3} - \frac{3519}{7}e$ |
| 23 | $[23, 23, w]$ | $-\frac{1}{4}e^{17} - \frac{119}{16}e^{15} - \frac{1431}{16}e^{13} - \frac{8901}{16}e^{11} - \frac{3803}{2}e^{9} - \frac{56155}{16}e^{7} - \frac{51925}{16}e^{5} - \frac{21601}{16}e^{3} - 206e$ |
| 23 | $[23, 23, w + 22]$ | $\phantom{-}\frac{51}{224}e^{17} + \frac{1507}{224}e^{15} + \frac{17943}{224}e^{13} + \frac{13737}{28}e^{11} + \frac{365977}{224}e^{9} + \frac{643507}{224}e^{7} + \frac{537093}{224}e^{5} + \frac{12603}{16}e^{3} + \frac{494}{7}e$ |
| 37 | $[37, 37, w + 18]$ | $-\frac{55}{448}e^{17} - \frac{1665}{448}e^{15} - \frac{20509}{448}e^{13} - \frac{66011}{224}e^{11} - \frac{474861}{448}e^{9} - \frac{948225}{448}e^{7} - \frac{989959}{448}e^{5} - 1070e^{3} - \frac{1238}{7}e$ |
| 41 | $[41, 41, -2w + 13]$ | $\phantom{-}\frac{3}{16}e^{16} + \frac{89}{16}e^{14} + \frac{1069}{16}e^{12} + \frac{3331}{8}e^{10} + \frac{22949}{16}e^{8} + \frac{43201}{16}e^{6} + \frac{41755}{16}e^{4} + 1176e^{2} + 193$ |
| 41 | $[41, 41, -2w - 11]$ | $\phantom{-}\frac{55}{112}e^{16} + \frac{1637}{112}e^{14} + \frac{19697}{112}e^{12} + \frac{61307}{56}e^{10} + \frac{419505}{112}e^{8} + \frac{774821}{112}e^{6} + \frac{714439}{112}e^{4} + 2595e^{2} + \frac{2607}{7}$ |
| 43 | $[43, 43, w + 11]$ | $-\frac{109}{224}e^{17} - \frac{3245}{224}e^{15} - \frac{39057}{224}e^{13} - \frac{7600}{7}e^{11} - \frac{832103}{224}e^{9} - \frac{1535829}{224}e^{7} - \frac{1413315}{224}e^{5} - \frac{40973}{16}e^{3} - \frac{2535}{7}e$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{167}{448}e^{17} - \frac{4997}{448}e^{15} - \frac{60577}{448}e^{13} - \frac{190625}{224}e^{11} - \frac{1326733}{448}e^{9} - \frac{2520565}{448}e^{7} - \frac{2443859}{448}e^{5} - \frac{38737}{16}e^{3} - \frac{2729}{7}e$ |
| 49 | $[49, 7, -7]$ | $-\frac{3}{56}e^{16} - \frac{87}{56}e^{14} - \frac{1011}{56}e^{12} - \frac{2993}{28}e^{10} - \frac{18915}{56}e^{8} - \frac{30239}{56}e^{6} - \frac{20327}{56}e^{4} - 62e^{2} + \frac{11}{7}$ |
| 71 | $[71, 71, -2w + 17]$ | $\phantom{-}\frac{97}{112}e^{16} + \frac{2883}{112}e^{14} + \frac{34635}{112}e^{12} + \frac{107591}{56}e^{10} + \frac{734071}{112}e^{8} + \frac{1348807}{112}e^{6} + \frac{1231109}{112}e^{4} + 4389e^{2} + \frac{4217}{7}$ |
| 71 | $[71, 71, -2w - 15]$ | $-\frac{5}{28}e^{16} - \frac{297}{56}e^{14} - \frac{1783}{28}e^{12} - \frac{22149}{56}e^{10} - \frac{75573}{56}e^{8} - \frac{69499}{28}e^{6} - \frac{127343}{56}e^{4} - 925e^{2} - \frac{941}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $\frac{31}{256}e^{17} + \frac{921}{256}e^{15} + \frac{11053}{256}e^{13} + \frac{34267}{128}e^{11} + \frac{232989}{256}e^{9} + \frac{425617}{256}e^{7} + \frac{384671}{256}e^{5} + \frac{18899}{32}e^{3} + 80e$ |