Properties

Label 2736.2.ds
Level $2736$
Weight $2$
Character orbit 2736.ds
Rep. character $\chi_{2736}(419,\cdot)$
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.ds (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

\( 1728q - 12q^{6} + O(q^{10}) \) \( 1728q - 12q^{6} + 24q^{12} + 20q^{18} - 24q^{24} + 24q^{27} + 40q^{30} + 28q^{36} + 48q^{39} - 40q^{42} - 52q^{48} - 864q^{49} - 156q^{50} + 40q^{51} + 112q^{54} - 36q^{58} + 72q^{59} - 136q^{60} + 72q^{64} - 152q^{66} - 156q^{68} + 60q^{72} - 40q^{78} + 72q^{82} - 120q^{83} - 208q^{84} - 120q^{86} - 48q^{88} + 8q^{90} - 228q^{92} + 48q^{93} + 16q^{96} - 32q^{99} + O(q^{100}) \)

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

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