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Properties

Label 3600.3.fq
Level $3600$
Weight $3$
Character orbit 3600.fq
Rep. character $\chi_{3600}(13,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $22976$
Sturm bound $2160$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3600.fq (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

\( 22976 q - 8 q^{2} - 20 q^{3} - 10 q^{4} - 8 q^{5} - 12 q^{6} - 32 q^{8} + O(q^{10}) \) \( 22976 q - 8 q^{2} - 20 q^{3} - 10 q^{4} - 8 q^{5} - 12 q^{6} - 32 q^{8} - 16 q^{10} - 6 q^{11} + 2 q^{12} - 10 q^{13} - 10 q^{14} - 32 q^{15} - 6 q^{16} - 64 q^{17} - 52 q^{18} - 40 q^{19} - 8 q^{20} + 78 q^{21} + 8 q^{22} - 72 q^{24} - 64 q^{26} - 20 q^{27} - 96 q^{28} - 10 q^{29} - 72 q^{30} - 12 q^{31} + 52 q^{32} - 32 q^{33} - 10 q^{34} - 432 q^{35} - 76 q^{36} - 40 q^{37} - 252 q^{38} + 72 q^{39} + 42 q^{40} + 362 q^{42} - 16 q^{43} - 40 q^{44} - 66 q^{45} - 24 q^{46} - 16 q^{47} + 52 q^{48} - 8 q^{50} - 32 q^{51} + 56 q^{52} - 24 q^{53} - 4 q^{54} - 6 q^{56} - 72 q^{57} - 24 q^{58} - 10 q^{59} + 2208 q^{60} - 6 q^{61} - 228 q^{62} - 228 q^{63} - 40 q^{64} - 16 q^{65} - 12 q^{66} - 6 q^{67} - 508 q^{68} + 16 q^{69} + 710 q^{72} - 16 q^{74} + 226 q^{75} - 16 q^{76} - 594 q^{77} + 2338 q^{78} - 20 q^{79} + 136 q^{80} - 24 q^{81} - 16 q^{82} - 10 q^{83} - 92 q^{84} - 58 q^{85} + 74 q^{86} + 36 q^{87} + 96 q^{88} + 912 q^{90} + 956 q^{91} + 42 q^{92} - 10 q^{94} - 16 q^{95} + 78 q^{96} - 16 q^{97} - 1660 q^{98} + O(q^{100}) \)

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.