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Properties

Label 3600.3.dd
Level $3600$
Weight $3$
Character orbit 3600.dd
Rep. character $\chi_{3600}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $3440$
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.dd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
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 3472 2336
Cusp forms 5712 3440 2272
Eisenstein series 96 32 64

Trace form

\( 3440 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 8 q^{8} + O(q^{10}) \) \( 3440 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 8 q^{8} - 4 q^{11} - 14 q^{12} + 4 q^{13} - 4 q^{16} + 16 q^{17} + 24 q^{18} - 8 q^{21} - 14 q^{22} - 72 q^{24} - 208 q^{26} + 8 q^{27} - 56 q^{28} - 8 q^{31} - 58 q^{32} + 8 q^{33} + 24 q^{34} + 56 q^{36} + 16 q^{37} - 258 q^{38} + 72 q^{39} - 230 q^{42} - 1152 q^{44} - 352 q^{46} + 4 q^{47} - 142 q^{48} - 8 q^{51} - 62 q^{52} - 336 q^{54} - 4 q^{56} + 72 q^{57} + 18 q^{58} - 4 q^{61} + 172 q^{62} - 188 q^{63} - 528 q^{64} - 840 q^{66} + 438 q^{68} + 36 q^{69} + 210 q^{72} - 1024 q^{74} + 308 q^{76} + 570 q^{78} - 16 q^{81} + 24 q^{82} + 4 q^{83} - 144 q^{84} - 4 q^{86} - 36 q^{87} - 150 q^{88} - 16 q^{91} + 52 q^{92} - 28 q^{93} - 1560 q^{96} + 4 q^{97} + 1196 q^{98} + 256 q^{99} + O(q^{100}) \)

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

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