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Properties

Label 64.22.i
Level $64$
Weight $22$
Character orbit 64.i
Rep. character $\chi_{64}(5,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1336$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 64.i (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(64, [\chi])\).

Total New Old
Modular forms 1352 1352 0
Cusp forms 1336 1336 0
Eisenstein series 16 16 0

Trace form

\( 1336 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 1336 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 207411361090032 q^{22} - 8 q^{23} - 1945658207807008 q^{24} - 8 q^{25} - 1506625290169968 q^{26} - 8 q^{27} + 11978218049315072 q^{28} - 8 q^{29} - 16217339993829528 q^{30} - 12832721772527328 q^{32} + 58324591899126992 q^{34} - 8 q^{35} - 296417618048471928 q^{36} - 8 q^{37} + 303109027666885872 q^{38} - 8 q^{39} - 363206157537854368 q^{40} - 8 q^{41} - 980887809273580528 q^{42} - 8 q^{43} - 959490752542847008 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 4761634387503570032 q^{50} - 3545471896164757736 q^{51} - 8655710943494332664 q^{52} - 8 q^{53} - 4994095300087806152 q^{54} + 15854219360527201336 q^{55} + 13445791338293702016 q^{56} - 8 q^{57} - 24235593818026622336 q^{58} + 24754986281321966136 q^{59} + 34373655846659160856 q^{60} - 8 q^{61} - 9454210277557709848 q^{62} + 78794423350543267904 q^{63} - 28235118983318354024 q^{64} - 16 q^{65} + 111234197313377019992 q^{66} + 68269055492132471752 q^{67} - 104659289810037971960 q^{68} - 8 q^{69} + 279305961159540045016 q^{70} - 135249633480998712264 q^{71} - 215147916304966389392 q^{72} - 8 q^{73} + 149453752937774472816 q^{74} - 466818284814457945544 q^{75} - 235541415539266676552 q^{76} - 8 q^{77} + 226776658842727689328 q^{78} - 30165378332775080936 q^{79} - 860612604870301954912 q^{80} - 8 q^{81} - 708517628372968195928 q^{82} - 8 q^{83} + 1424936216815736264744 q^{84} - 8 q^{85} - 917406725370159511248 q^{86} - 8 q^{87} - 418946962671126792248 q^{88} - 8 q^{89} + 4037191479561093749992 q^{90} - 8 q^{91} - 6603731275935646802256 q^{92} + 83682825616 q^{93} + 2424473717652338934808 q^{94} + 4329988420061566228352 q^{96} - 11226390629590293575056 q^{98} + 83682825616 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.