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Properties

Label 3600.2.fr
Level $3600$
Weight $2$
Character orbit 3600.fr
Rep. character $\chi_{3600}(173,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $11456$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3600.fr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3600 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3600, [\chi])\).

Total New Old
Modular forms 11584 11584 0
Cusp forms 11456 11456 0
Eisenstein series 128 128 0

Trace form

\( 11456 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} + O(q^{10}) \) \( 11456 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 40 q^{10} - 18 q^{11} - 10 q^{12} - 10 q^{13} - 30 q^{14} - 32 q^{15} - 6 q^{16} - 40 q^{18} - 40 q^{19} - 24 q^{20} + 18 q^{21} - 16 q^{22} + 24 q^{24} - 20 q^{27} - 48 q^{28} - 30 q^{29} - 48 q^{30} - 12 q^{31} - 84 q^{32} - 32 q^{33} - 10 q^{34} - 28 q^{36} - 40 q^{37} - 12 q^{38} + 24 q^{39} - 18 q^{40} + 26 q^{42} - 16 q^{43} - 6 q^{45} - 24 q^{46} - 48 q^{47} - 128 q^{48} - 24 q^{50} - 32 q^{51} + 8 q^{52} - 28 q^{54} - 18 q^{56} - 24 q^{57} - 30 q^{59} - 132 q^{60} - 6 q^{61} - 60 q^{63} - 40 q^{64} - 48 q^{65} - 12 q^{66} - 6 q^{67} - 32 q^{69} - 12 q^{70} + 2 q^{72} - 24 q^{74} + 46 q^{75} - 16 q^{76} - 18 q^{77} - 158 q^{78} - 20 q^{79} - 24 q^{81} - 40 q^{82} - 30 q^{83} - 44 q^{84} + 2 q^{85} - 18 q^{86} - 12 q^{87} + 24 q^{90} + 116 q^{91} + 90 q^{92} - 10 q^{94} - 48 q^{95} - 42 q^{96} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

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