Properties

Label 3600.3.gd
Level $3600$
Weight $3$
Character orbit 3600.gd
Rep. character $\chi_{3600}(221,\cdot)$
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.gd (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

\( 22976 q - 18 q^{2} - 12 q^{3} - 6 q^{4} - 24 q^{5} - 12 q^{6} + O(q^{10}) \) \( 22976 q - 18 q^{2} - 12 q^{3} - 6 q^{4} - 24 q^{5} - 12 q^{6} - 32 q^{10} - 18 q^{11} - 12 q^{12} - 6 q^{13} - 18 q^{14} - 32 q^{15} - 6 q^{16} - 48 q^{18} - 24 q^{19} - 150 q^{20} - 66 q^{21} - 6 q^{22} - 32 q^{24} - 12 q^{27} - 216 q^{28} - 18 q^{29} + 70 q^{30} - 12 q^{31} - 48 q^{32} - 24 q^{33} - 22 q^{34} - 248 q^{36} - 24 q^{37} - 18 q^{38} - 8 q^{40} - 228 q^{42} - 16 q^{43} - 66 q^{45} - 56 q^{46} - 36 q^{47} + 66 q^{48} + 79040 q^{49} - 258 q^{50} - 104 q^{51} - 6 q^{52} - 12 q^{54} - 900 q^{56} - 6 q^{58} - 18 q^{59} - 1080 q^{60} - 6 q^{61} - 612 q^{63} - 24 q^{64} - 48 q^{65} - 896 q^{66} - 6 q^{67} - 240 q^{68} - 48 q^{69} + 384 q^{70} + 80 q^{72} - 48 q^{74} - 222 q^{75} - 16 q^{76} - 18 q^{77} - 104 q^{78} - 12 q^{79} - 24 q^{81} - 96 q^{82} - 18 q^{83} - 1066 q^{84} - 58 q^{85} - 1818 q^{86} - 54 q^{88} + 328 q^{90} - 612 q^{91} + 666 q^{92} - 68 q^{93} + 26 q^{94} - 48 q^{95} - 12 q^{96} - 12 q^{97} - 356 q^{99} + O(q^{100}) \)

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

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