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Properties

Label 3600.3.do
Level $3600$
Weight $3$
Character orbit 3600.do
Rep. character $\chi_{3600}(101,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $3624$
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.do (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 5808 3672 2136
Cusp forms 5712 3624 2088
Eisenstein series 96 48 48

Trace form

\( 3624 q + 6 q^{2} + 4 q^{3} + 2 q^{4} - 18 q^{6} + O(q^{10}) \) \( 3624 q + 6 q^{2} + 4 q^{3} + 2 q^{4} - 18 q^{6} - 18 q^{11} - 56 q^{12} + 2 q^{13} + 6 q^{14} - 6 q^{16} + 46 q^{18} + 8 q^{19} + 6 q^{21} + 2 q^{22} - 120 q^{24} + 52 q^{27} + 72 q^{28} + 6 q^{29} - 12 q^{31} + 6 q^{32} + 8 q^{33} + 26 q^{34} - 74 q^{36} + 8 q^{37} + 6 q^{38} + 196 q^{42} + 2 q^{43} + 128 q^{46} + 12 q^{47} - 162 q^{48} + 12184 q^{49} - 128 q^{51} + 2 q^{52} + 102 q^{54} + 276 q^{56} - 88 q^{58} - 426 q^{59} - 6 q^{61} + 204 q^{63} + 260 q^{64} + 932 q^{66} + 2 q^{67} - 324 q^{68} + 58 q^{69} + 106 q^{72} + 258 q^{74} + 150 q^{76} + 6 q^{77} + 220 q^{78} + 4 q^{79} - 24 q^{81} - 404 q^{82} - 714 q^{83} + 210 q^{84} - 918 q^{86} - 22 q^{88} + 172 q^{91} + 348 q^{92} + 34 q^{93} - 46 q^{94} - 210 q^{96} + 4 q^{97} - 286 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)