Properties

Label 2736.2.gq
Level $2736$
Weight $2$
Character orbit 2736.gq
Rep. character $\chi_{2736}(131,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $5712$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.gq (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2736 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 5808 5808 0
Cusp forms 5712 5712 0
Eisenstein series 96 96 0

Trace form

\( 5712 q - 18 q^{2} - 12 q^{3} - 6 q^{4} - 18 q^{5} - 12 q^{6} + 12 q^{7} + O(q^{10}) \) \( 5712 q - 18 q^{2} - 12 q^{3} - 6 q^{4} - 18 q^{5} - 12 q^{6} + 12 q^{7} - 24 q^{10} - 6 q^{12} - 6 q^{13} - 18 q^{14} - 6 q^{16} - 24 q^{18} - 24 q^{19} - 36 q^{20} + 6 q^{21} - 6 q^{22} - 36 q^{23} - 12 q^{24} + 144 q^{26} - 6 q^{27} - 48 q^{28} - 18 q^{29} - 90 q^{30} - 18 q^{32} - 24 q^{33} - 6 q^{34} + 90 q^{35} - 12 q^{36} - 48 q^{37} - 18 q^{38} - 48 q^{39} - 6 q^{40} + 84 q^{42} - 6 q^{43} - 198 q^{44} - 6 q^{45} - 12 q^{46} - 12 q^{48} - 2700 q^{49} - 12 q^{51} - 6 q^{52} + 54 q^{54} - 48 q^{55} - 162 q^{56} - 12 q^{58} - 18 q^{59} - 96 q^{60} - 6 q^{61} + 36 q^{62} - 12 q^{64} - 132 q^{66} - 6 q^{67} - 18 q^{68} - 6 q^{69} + 78 q^{70} - 48 q^{72} - 270 q^{74} + 144 q^{75} - 6 q^{76} - 36 q^{77} - 24 q^{78} - 24 q^{81} - 24 q^{82} - 18 q^{83} + 78 q^{84} - 6 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} + 96 q^{90} - 66 q^{91} - 18 q^{92} + 24 q^{93} - 12 q^{94} - 174 q^{96} - 12 q^{97} + 162 q^{98} - 120 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.