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Properties

Label 3600.2.dj
Level $3600$
Weight $2$
Character orbit 3600.dj
Rep. character $\chi_{3600}(643,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
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.dj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2928 1744 1184
Cusp forms 2832 1712 1120
Eisenstein series 96 32 64

Trace form

\( 1712 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 4 q^{7} + 8 q^{8} + O(q^{10}) \) \( 1712 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 4 q^{7} + 8 q^{8} - 4 q^{11} - 2 q^{12} - 4 q^{16} + 16 q^{17} + 28 q^{18} - 8 q^{21} - 6 q^{22} + 4 q^{23} - 24 q^{24} - 80 q^{26} + 8 q^{27} + 24 q^{28} - 18 q^{32} + 8 q^{33} + 24 q^{34} + 8 q^{36} + 26 q^{38} + 30 q^{42} + 128 q^{44} - 64 q^{46} + 10 q^{48} - 8 q^{51} + 18 q^{52} + 16 q^{53} + 40 q^{54} - 4 q^{56} + 24 q^{57} - 6 q^{58} - 4 q^{61} - 44 q^{62} - 48 q^{64} + 56 q^{66} - 58 q^{68} + 12 q^{69} - 32 q^{71} + 26 q^{72} - 104 q^{74} + 20 q^{76} - 52 q^{77} - 58 q^{78} - 16 q^{81} + 16 q^{82} + 4 q^{83} + 48 q^{84} - 4 q^{86} + 64 q^{87} - 38 q^{88} - 16 q^{91} - 20 q^{92} + 104 q^{96} + 4 q^{97} + 196 q^{98} + 64 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

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