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Properties

Label 3600.3.fg
Level $3600$
Weight $3$
Character orbit 3600.fg
Rep. character $\chi_{3600}(29,\cdot)$
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.fg (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

\( 22976 q - 30 q^{2} - 20 q^{3} - 6 q^{4} - 24 q^{5} - 12 q^{6} + O(q^{10}) \) \( 22976 q - 30 q^{2} - 20 q^{3} - 6 q^{4} - 24 q^{5} - 12 q^{6} - 32 q^{10} - 18 q^{11} - 20 q^{12} - 10 q^{13} - 18 q^{14} - 32 q^{15} - 6 q^{16} - 24 q^{19} + 102 q^{20} + 42 q^{21} - 10 q^{22} - 32 q^{24} - 20 q^{27} + 280 q^{28} - 18 q^{29} - 142 q^{30} - 12 q^{31} - 40 q^{33} + 10 q^{34} + 352 q^{36} - 40 q^{37} - 30 q^{38} - 8 q^{40} + 340 q^{42} - 66 q^{45} + 8 q^{46} - 60 q^{47} + 110 q^{48} - 79104 q^{49} + 210 q^{50} + 40 q^{51} - 10 q^{52} - 12 q^{54} + 864 q^{56} - 10 q^{58} - 18 q^{59} - 2536 q^{60} - 6 q^{61} + 940 q^{63} - 24 q^{64} - 48 q^{65} + 872 q^{66} - 10 q^{67} + 24 q^{69} - 400 q^{70} - 20 q^{72} - 48 q^{74} - 258 q^{75} - 16 q^{76} - 30 q^{77} - 20 q^{78} - 12 q^{79} - 24 q^{81} - 30 q^{83} - 478 q^{84} + 42 q^{85} + 1782 q^{86} - 10 q^{88} - 348 q^{90} + 564 q^{91} - 30 q^{92} - 38 q^{94} - 48 q^{95} - 12 q^{96} - 20 q^{97} - 356 q^{99} + O(q^{100}) \)

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.