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Properties

Label 2736.2.em
Level $2736$
Weight $2$
Character orbit 2736.em
Rep. character $\chi_{2736}(293,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1904$
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.em (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2736 \)
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 1936 0
Cusp forms 1904 1904 0
Eisenstein series 32 32 0

Trace form

\( 1904 q - 12 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 2 q^{6} + O(q^{10}) \) \( 1904 q - 12 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 2 q^{6} - 12 q^{10} - 12 q^{11} - 6 q^{14} - 12 q^{15} - 4 q^{16} + 12 q^{18} - 8 q^{19} - 54 q^{20} - 24 q^{21} - 6 q^{22} - 34 q^{24} - 12 q^{28} - 6 q^{29} + 16 q^{30} - 12 q^{32} - 12 q^{33} - 6 q^{34} + 30 q^{35} + 30 q^{36} - 6 q^{38} - 6 q^{40} - 66 q^{42} - 4 q^{43} - 66 q^{44} - 18 q^{45} - 12 q^{47} - 6 q^{48} + 896 q^{49} - 6 q^{51} + 20 q^{54} - 4 q^{58} - 6 q^{59} + 36 q^{60} + 2 q^{61} - 12 q^{62} - 60 q^{63} - 16 q^{64} - 22 q^{66} - 36 q^{68} - 18 q^{69} + 36 q^{70} + 126 q^{72} - 48 q^{75} + 10 q^{76} - 12 q^{77} + 6 q^{78} + 48 q^{80} - 4 q^{81} + 4 q^{82} - 12 q^{83} - 44 q^{85} - 12 q^{86} - 6 q^{90} - 54 q^{91} - 14 q^{93} - 24 q^{94} - 12 q^{95} - 132 q^{96} - 54 q^{98} + 2 q^{99} + O(q^{100}) \)

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.