Properties

Label 2736.2.gm
Level $2736$
Weight $2$
Character orbit 2736.gm
Rep. character $\chi_{2736}(85,\cdot)$
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.gm (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

\( 5712q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{5} - 12q^{6} - 12q^{8} + O(q^{10}) \) \( 5712q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{5} - 12q^{6} - 12q^{8} - 24q^{10} + 6q^{11} - 6q^{12} - 6q^{13} + 42q^{14} - 24q^{15} - 6q^{16} - 48q^{17} - 24q^{18} - 24q^{19} - 12q^{20} + 24q^{21} - 6q^{22} - 12q^{24} + 36q^{26} - 6q^{27} - 6q^{29} + 36q^{30} + 12q^{31} - 6q^{32} - 24q^{33} - 6q^{34} + 6q^{35} - 12q^{36} - 48q^{37} - 6q^{38} - 6q^{40} + 120q^{42} - 6q^{43} - 90q^{44} - 6q^{45} - 12q^{46} - 12q^{47} - 12q^{48} - 5448q^{49} + 6q^{50} - 12q^{51} - 6q^{52} - 24q^{53} - 144q^{54} - 54q^{56} - 12q^{58} - 6q^{59} + 30q^{60} - 6q^{61} - 36q^{62} + 144q^{63} - 12q^{64} + 12q^{65} - 72q^{66} - 6q^{67} - 12q^{68} - 6q^{69} + 36q^{70} - 144q^{72} - 174q^{74} - 192q^{75} - 6q^{76} + 72q^{77} - 24q^{78} - 12q^{79} - 24q^{80} - 24q^{81} - 24q^{82} - 12q^{83} + 162q^{84} - 6q^{85} - 6q^{86} - 12q^{88} - 228q^{90} + 18q^{91} - 6q^{92} + 6q^{93} - 12q^{94} - 12q^{95} - 78q^{96} - 12q^{97} + 6q^{98} - 66q^{99} + O(q^{100}) \)

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

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