Properties

Label 2736.2.eq
Level $2736$
Weight $2$
Character orbit 2736.eq
Rep. character $\chi_{2736}(1171,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $792$
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.eq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1952 808 1144
Cusp forms 1888 792 1096
Eisenstein series 64 16 48

Trace form

\( 792q + 6q^{2} - 2q^{4} + 2q^{5} - 16q^{7} + O(q^{10}) \) \( 792q + 6q^{2} - 2q^{4} + 2q^{5} - 16q^{7} + 8q^{11} - 6q^{13} + 18q^{14} - 6q^{16} + 4q^{17} + 4q^{19} - 20q^{20} - 6q^{22} + 4q^{23} - 4q^{26} - 30q^{28} + 6q^{29} - 24q^{32} + 24q^{34} - 12q^{35} - 30q^{38} + 24q^{40} - 2q^{43} + 52q^{44} + 728q^{49} - 54q^{52} + 6q^{53} - 4q^{55} - 36q^{58} + 6q^{59} + 30q^{61} + 62q^{62} - 44q^{64} - 6q^{67} + 8q^{68} + 24q^{70} + 12q^{71} + 50q^{74} + 30q^{76} + 64q^{77} - 14q^{80} + 66q^{82} - 32q^{83} + 34q^{85} + 6q^{86} - 48q^{91} - 26q^{92} - 12q^{97} + 102q^{98} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)