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Properties

Label 3600.3.de
Level $3600$
Weight $3$
Character orbit 3600.de
Rep. character $\chi_{3600}(443,\cdot)$
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.de (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

\( 3440 q + 6 q^{2} - 8 q^{6} + 4 q^{7} + O(q^{10}) \) \( 3440 q + 6 q^{2} - 8 q^{6} + 4 q^{7} - 12 q^{11} + 22 q^{12} + 4 q^{13} - 4 q^{16} - 16 q^{18} - 8 q^{21} - 14 q^{22} + 12 q^{23} - 72 q^{24} + 72 q^{28} - 174 q^{32} + 8 q^{33} + 24 q^{34} + 56 q^{36} + 16 q^{37} + 30 q^{38} - 358 q^{42} + 4 q^{43} + 320 q^{46} - 106 q^{48} - 8 q^{51} - 62 q^{52} + 368 q^{54} - 12 q^{56} - 72 q^{57} - 14 q^{58} - 4 q^{61} + 528 q^{64} + 824 q^{66} + 4 q^{67} + 102 q^{68} + 36 q^{69} - 722 q^{72} - 48 q^{74} - 316 q^{76} - 650 q^{78} - 16 q^{81} - 8 q^{82} - 12 q^{86} - 440 q^{87} - 102 q^{88} - 16 q^{91} - 336 q^{92} + 44 q^{93} + 1544 q^{96} + 4 q^{97} - 256 q^{99} + O(q^{100}) \)

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

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