Properties

Label 2736.2.en
Level $2736$
Weight $2$
Character orbit 2736.en
Rep. character $\chi_{2736}(229,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1728$
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.en (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
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 1936 1728 208
Cusp forms 1904 1728 176
Eisenstein series 32 0 32

Trace form

\( 1728q + 12q^{6} + O(q^{10}) \) \( 1728q + 12q^{6} - 24q^{12} + 20q^{18} + 56q^{24} + 32q^{26} - 24q^{27} - 40q^{30} + 40q^{32} - 52q^{36} + 40q^{42} + 80q^{47} - 52q^{48} + 864q^{49} + 52q^{50} + 40q^{51} - 112q^{54} + 36q^{58} - 24q^{59} - 24q^{60} - 24q^{62} + 72q^{64} - 88q^{66} - 52q^{68} - 60q^{72} - 192q^{78} - 272q^{80} + 72q^{82} + 40q^{83} + 96q^{84} - 144q^{86} + 48q^{88} - 8q^{90} + 76q^{92} + 48q^{93} - 64q^{95} - 16q^{96} - 32q^{99} + O(q^{100}) \)

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

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

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

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)