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Properties

Label 3600.2.dr
Level $3600$
Weight $2$
Character orbit 3600.dr
Rep. character $\chi_{3600}(301,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1800$
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.dr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
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 1848 1080
Cusp forms 2832 1800 1032
Eisenstein series 96 48 48

Trace form

\( 1800 q + 2 q^{2} + 4 q^{3} + 2 q^{4} - 18 q^{6} + 8 q^{8} + O(q^{10}) \) \( 1800 q + 2 q^{2} + 4 q^{3} + 2 q^{4} - 18 q^{6} + 8 q^{8} - 6 q^{11} + 16 q^{12} + 2 q^{13} - 22 q^{14} - 6 q^{16} + 16 q^{17} - 2 q^{18} + 8 q^{19} - 6 q^{21} + 2 q^{22} + 8 q^{26} + 16 q^{27} + 24 q^{28} + 2 q^{29} - 12 q^{31} - 18 q^{32} + 8 q^{33} - 10 q^{34} - 50 q^{36} + 8 q^{37} - 26 q^{38} + 16 q^{42} + 2 q^{43} + 52 q^{44} - 40 q^{46} - 36 q^{47} - 42 q^{48} + 832 q^{49} - 20 q^{51} + 2 q^{52} + 8 q^{53} - 30 q^{54} + 20 q^{56} - 16 q^{58} + 14 q^{59} - 6 q^{61} + 100 q^{62} + 36 q^{63} - 28 q^{64} - 64 q^{66} + 2 q^{67} + 36 q^{68} - 14 q^{69} - 2 q^{72} + 30 q^{74} - 18 q^{76} + 30 q^{77} + 28 q^{78} + 4 q^{79} - 24 q^{81} - 20 q^{82} - 18 q^{83} + 54 q^{84} + 26 q^{86} + 26 q^{88} + 4 q^{91} + 56 q^{92} - 26 q^{93} + 26 q^{94} - 66 q^{96} + 4 q^{97} + 96 q^{98} - 10 q^{99} + O(q^{100}) \)

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

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