↑

Properties

Label 3600.3.fh
Level $3600$
Weight $3$
Character orbit 3600.fh
Rep. character $\chi_{3600}(211,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $22976$
Sturm bound $2160$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3600.fh (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3600 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).

Total New Old
Modular forms 23104 23104 0
Cusp forms 22976 22976 0
Eisenstein series 128 128 0

Trace form

\( 22976 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 8 q^{5} - 12 q^{6} - 32 q^{7} - 24 q^{8} + O(q^{10}) \) \( 22976 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 8 q^{5} - 12 q^{6} - 32 q^{7} - 24 q^{8} - 32 q^{10} - 6 q^{11} - 12 q^{12} - 6 q^{13} + 42 q^{14} - 6 q^{16} - 48 q^{17} - 16 q^{18} - 24 q^{19} + 34 q^{20} + 42 q^{21} - 6 q^{22} - 12 q^{23} - 32 q^{24} - 64 q^{26} - 12 q^{27} + 168 q^{28} - 6 q^{29} + 110 q^{30} - 16 q^{32} - 24 q^{33} + 10 q^{34} + 368 q^{35} + 352 q^{36} - 24 q^{37} - 762 q^{38} - 24 q^{39} - 8 q^{40} + 204 q^{42} - 16 q^{43} - 24 q^{44} + 34 q^{45} - 56 q^{46} + 66 q^{48} - 79104 q^{49} + 86 q^{50} + 40 q^{51} - 6 q^{52} - 24 q^{53} - 12 q^{54} - 64 q^{55} - 300 q^{56} - 6 q^{58} - 6 q^{59} - 1016 q^{60} - 6 q^{61} + 8 q^{62} - 24 q^{64} - 16 q^{65} - 928 q^{66} - 6 q^{67} + 48 q^{68} - 48 q^{69} - 400 q^{70} - 48 q^{71} - 104 q^{72} - 16 q^{74} + 226 q^{75} - 16 q^{76} + 582 q^{77} + 48 q^{78} - 1112 q^{80} - 24 q^{81} - 32 q^{82} - 6 q^{83} + 1042 q^{84} + 42 q^{85} - 606 q^{86} + 872 q^{87} + 42 q^{88} - 1008 q^{90} + 564 q^{91} - 362 q^{92} + 4 q^{93} + 26 q^{94} - 12 q^{96} - 12 q^{97} + 612 q^{98} + 292 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

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