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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

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

Display 100 coefficients 10 coefficients

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

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