Base field \(\Q(\sqrt{417}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 104\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,w + 10]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} + x^{16} - 28x^{15} - 28x^{14} + 317x^{13} + 312x^{12} - 1873x^{11} - 1777x^{10} + 6220x^{9} + 5560x^{8} - 11573x^{7} - 9623x^{6} + 10966x^{5} + 8723x^{4} - 3662x^{3} - 3388x^{2} - 416x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 107w - 1146]$ | $-1$ |
| 2 | $[2, 2, 107w + 1039]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 1108w - 11867]$ | $-1$ |
| 7 | $[7, 7, 38w - 407]$ | $\phantom{-}\frac{7}{4}e^{16} - \frac{3}{4}e^{15} - \frac{183}{4}e^{14} + \frac{69}{4}e^{13} + 474e^{12} - \frac{627}{4}e^{11} - \frac{9951}{4}e^{10} + \frac{1449}{2}e^{9} + \frac{28055}{4}e^{8} - \frac{3545}{2}e^{7} - \frac{20723}{2}e^{6} + \frac{7807}{4}e^{5} + \frac{14363}{2}e^{4} - \frac{693}{2}e^{3} - 1870e^{2} - 265e + 8$ |
| 7 | $[7, 7, -38w - 369]$ | $-\frac{25}{16}e^{16} + \frac{15}{8}e^{15} + 41e^{14} - \frac{369}{8}e^{13} - \frac{6869}{16}e^{12} + \frac{7145}{16}e^{11} + \frac{18427}{8}e^{10} - \frac{34667}{16}e^{9} - \frac{108229}{16}e^{8} + \frac{87847}{16}e^{7} + \frac{86087}{8}e^{6} - \frac{105971}{16}e^{5} - \frac{138333}{16}e^{4} + \frac{20063}{8}e^{3} + \frac{6053}{2}e^{2} + \frac{1449}{4}e - \frac{55}{4}$ |
| 13 | $[13, 13, -4w - 39]$ | $\phantom{-}\frac{17}{4}e^{16} - \frac{9}{4}e^{15} - \frac{887}{8}e^{14} + \frac{209}{4}e^{13} + \frac{9173}{8}e^{12} - \frac{1909}{4}e^{11} - \frac{12021}{2}e^{10} + \frac{17585}{8}e^{9} + 16943e^{8} - \frac{10625}{2}e^{7} - \frac{200599}{8}e^{6} + \frac{46675}{8}e^{5} + \frac{139983}{8}e^{4} - \frac{5077}{4}e^{3} - 4651e^{2} - \frac{1307}{2}e + \frac{37}{2}$ |
| 13 | $[13, 13, 4w - 43]$ | $-\frac{11}{8}e^{16} + \frac{7}{4}e^{15} + \frac{289}{8}e^{14} - \frac{173}{4}e^{13} - 379e^{12} + \frac{3367}{8}e^{11} + \frac{4079}{2}e^{10} - \frac{8213}{4}e^{9} - \frac{48137}{8}e^{8} + \frac{41881}{8}e^{7} + \frac{77165}{8}e^{6} - \frac{25505}{4}e^{5} - \frac{31453}{4}e^{4} + 2486e^{3} + \frac{5655}{2}e^{2} + 323e - 13$ |
| 17 | $[17, 17, 2w + 19]$ | $\phantom{-}\frac{29}{16}e^{16} - \frac{31}{8}e^{15} - \frac{389}{8}e^{14} + \frac{781}{8}e^{13} + \frac{8427}{16}e^{12} - \frac{15469}{16}e^{11} - \frac{23757}{8}e^{10} + \frac{76497}{16}e^{9} + \frac{149621}{16}e^{8} - \frac{196803}{16}e^{7} - \frac{65485}{4}e^{6} + \frac{242497}{16}e^{5} + \frac{240703}{16}e^{4} - \frac{49193}{8}e^{3} - \frac{12429}{2}e^{2} - \frac{3079}{4}e + \frac{105}{4}$ |
| 17 | $[17, 17, -2w + 21]$ | $-\frac{29}{8}e^{16} + 3e^{15} + \frac{759}{8}e^{14} - \frac{145}{2}e^{13} - \frac{1975}{2}e^{12} + \frac{5525}{8}e^{11} + \frac{20951}{4}e^{10} - \frac{13241}{4}e^{9} - \frac{120607}{8}e^{8} + \frac{66541}{8}e^{7} + \frac{185389}{8}e^{6} - \frac{19699}{2}e^{5} - \frac{69943}{4}e^{4} + 3352e^{3} + \frac{10997}{2}e^{2} + 687e - 27$ |
| 23 | $[23, 23, -24w - 233]$ | $-\frac{71}{16}e^{16} + \frac{5}{2}e^{15} + \frac{925}{8}e^{14} - \frac{233}{4}e^{13} - \frac{19109}{16}e^{12} + \frac{8539}{16}e^{11} + \frac{12509}{2}e^{10} - \frac{39419}{16}e^{9} - \frac{282031}{16}e^{8} + \frac{95483}{16}e^{7} + \frac{209049}{8}e^{6} - \frac{105873}{16}e^{5} - \frac{293837}{16}e^{4} + \frac{12739}{8}e^{3} + 4991e^{2} + \frac{2683}{4}e - \frac{111}{4}$ |
| 23 | $[23, 23, 24w - 257]$ | $\phantom{-}\frac{69}{16}e^{16} - \frac{43}{8}e^{15} - \frac{455}{4}e^{14} + \frac{1061}{8}e^{13} + \frac{19189}{16}e^{12} - \frac{20597}{16}e^{11} - \frac{51939}{8}e^{10} + \frac{100075}{16}e^{9} + \frac{308489}{16}e^{8} - \frac{253443}{16}e^{7} - \frac{248677}{8}e^{6} + \frac{304619}{16}e^{5} + \frac{405765}{16}e^{4} - \frac{56575}{8}e^{3} - \frac{17993}{2}e^{2} - \frac{4625}{4}e + \frac{159}{4}$ |
| 25 | $[25, 5, -5]$ | $-\frac{25}{4}e^{16} + \frac{59}{8}e^{15} + \frac{1317}{8}e^{14} - \frac{1455}{8}e^{13} - \frac{13855}{8}e^{12} + 1766e^{11} + \frac{74759}{8}e^{10} - \frac{68761}{8}e^{9} - 27630e^{8} + \frac{174667}{8}e^{7} + 44309e^{6} - 26313e^{5} - \frac{287451}{8}e^{4} + \frac{38885}{4}e^{3} + \frac{25351}{2}e^{2} + 1679e - \frac{83}{2}$ |
| 31 | $[31, 31, -894w - 8681]$ | $\phantom{-}\frac{27}{8}e^{16} - \frac{11}{8}e^{15} - \frac{705}{8}e^{14} + \frac{251}{8}e^{13} + \frac{1823}{2}e^{12} - \frac{2261}{8}e^{11} - \frac{38183}{8}e^{10} + \frac{2591}{2}e^{9} + \frac{107309}{8}e^{8} - \frac{6291}{2}e^{7} - 19728e^{6} + \frac{27293}{8}e^{5} + \frac{27143}{2}e^{4} - \frac{1039}{2}e^{3} - 3477e^{2} - \frac{969}{2}e + 17$ |
| 31 | $[31, 31, -894w + 9575]$ | $\phantom{-}\frac{17}{16}e^{16} - \frac{17}{8}e^{15} - \frac{113}{4}e^{14} + \frac{423}{8}e^{13} + \frac{4849}{16}e^{12} - \frac{8257}{16}e^{11} - \frac{13549}{8}e^{10} + \frac{40159}{16}e^{9} + \frac{84845}{16}e^{8} - \frac{101403}{16}e^{7} - \frac{74299}{8}e^{6} + \frac{122067}{16}e^{5} + \frac{137377}{16}e^{4} - \frac{23407}{8}e^{3} - \frac{7045}{2}e^{2} - \frac{2077}{4}e + \frac{47}{4}$ |
| 37 | $[37, 37, 252w - 2699]$ | $\phantom{-}\frac{5}{16}e^{16} - \frac{11}{8}e^{15} - \frac{69}{8}e^{14} + \frac{281}{8}e^{13} + \frac{1563}{16}e^{12} - \frac{5637}{16}e^{11} - \frac{4693}{8}e^{10} + \frac{28169}{16}e^{9} + \frac{32045}{16}e^{8} - \frac{73083}{16}e^{7} - \frac{15467}{4}e^{6} + \frac{91217}{16}e^{5} + \frac{64303}{16}e^{4} - \frac{19437}{8}e^{3} - 1926e^{2} - \frac{907}{4}e + \frac{41}{4}$ |
| 37 | $[37, 37, 252w + 2447]$ | $\phantom{-}\frac{33}{8}e^{16} - \frac{17}{8}e^{15} - \frac{215}{2}e^{14} + \frac{393}{8}e^{13} + \frac{8881}{8}e^{12} - \frac{3571}{8}e^{11} - \frac{46463}{8}e^{10} + \frac{16357}{8}e^{9} + \frac{130633}{8}e^{8} - 4913e^{7} - \frac{192639}{8}e^{6} + \frac{10685}{2}e^{5} + \frac{133651}{8}e^{4} - \frac{4383}{4}e^{3} - 4386e^{2} - 606e + \frac{31}{2}$ |
| 53 | $[53, 53, -1322w - 12837]$ | $-\frac{7}{16}e^{16} + \frac{11}{8}e^{15} + \frac{97}{8}e^{14} - \frac{285}{8}e^{13} - \frac{2189}{16}e^{12} + \frac{5823}{16}e^{11} + \frac{6481}{8}e^{10} - \frac{29775}{16}e^{9} - \frac{43159}{16}e^{8} + \frac{79365}{16}e^{7} + \frac{20099}{4}e^{6} - \frac{101867}{16}e^{5} - \frac{79577}{16}e^{4} + \frac{22267}{8}e^{3} + 2273e^{2} + \frac{957}{4}e - \frac{63}{4}$ |
| 53 | $[53, 53, 1322w - 14159]$ | $-\frac{175}{16}e^{16} + \frac{75}{8}e^{15} + \frac{2291}{8}e^{14} - \frac{1813}{8}e^{13} - \frac{47737}{16}e^{12} + \frac{34519}{16}e^{11} + \frac{126845}{8}e^{10} - \frac{165099}{16}e^{9} - \frac{732871}{16}e^{8} + \frac{413069}{16}e^{7} + \frac{141761}{2}e^{6} - \frac{485479}{16}e^{5} - \frac{866109}{16}e^{4} + \frac{80351}{8}e^{3} + 17289e^{2} + \frac{9517}{4}e - \frac{267}{4}$ |
| 59 | $[59, 59, -100w - 971]$ | $\phantom{-}7e^{16} - \frac{11}{2}e^{15} - \frac{733}{4}e^{14} + \frac{265}{2}e^{13} + \frac{7629}{4}e^{12} - 1258e^{11} - 10110e^{10} + \frac{24037}{4}e^{9} + \frac{58101}{2}e^{8} - \frac{30073}{2}e^{7} - \frac{177905}{4}e^{6} + \frac{70575}{4}e^{5} + \frac{132919}{4}e^{4} - \frac{11509}{2}e^{3} - 10210e^{2} - 1323e + 39$ |
| 59 | $[59, 59, 100w - 1071]$ | $-\frac{25}{8}e^{16} + \frac{11}{2}e^{15} + \frac{331}{4}e^{14} - 137e^{13} - \frac{7043}{8}e^{12} + \frac{10725}{8}e^{11} + \frac{9695}{2}e^{10} - \frac{52405}{8}e^{9} - \frac{118537}{8}e^{8} + \frac{133209}{8}e^{7} + \frac{100121}{4}e^{6} - \frac{161603}{8}e^{5} - \frac{176259}{8}e^{4} + \frac{31541}{4}e^{3} + 8665e^{2} + \frac{2299}{2}e - \frac{45}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-107w + 1146]$ | $1$ |
| $3$ | $[3,3,-1108w - 10759]$ | $1$ |