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Properties

Label 2736.2.ef
Level $2736$
Weight $2$
Character orbit 2736.ef
Rep. character $\chi_{2736}(349,\cdot)$
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.ef (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

\( 1904 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 16 q^{8} + O(q^{10}) \) \( 1904 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 16 q^{8} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} + 10 q^{14} - 4 q^{15} - 4 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 18 q^{20} + 4 q^{21} + 2 q^{22} + 30 q^{24} - 48 q^{26} - 8 q^{27} - 12 q^{28} + 2 q^{29} - 40 q^{30} - 8 q^{31} - 4 q^{32} - 4 q^{33} - 6 q^{34} - 14 q^{35} + 30 q^{36} - 16 q^{37} - 58 q^{38} + 2 q^{40} + 14 q^{42} - 4 q^{43} + 18 q^{44} + 2 q^{45} - 32 q^{46} + 4 q^{47} - 42 q^{48} + 896 q^{49} + 4 q^{50} + 10 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{54} - 16 q^{56} - 4 q^{58} + 2 q^{59} - 48 q^{60} + 2 q^{61} - 88 q^{62} - 60 q^{63} - 16 q^{64} - 8 q^{65} + 18 q^{66} - 4 q^{67} + 4 q^{68} - 2 q^{69} - 12 q^{70} + 42 q^{72} + 52 q^{74} + 100 q^{75} + 10 q^{76} - 60 q^{77} + 2 q^{78} - 8 q^{79} - 20 q^{80} - 4 q^{81} + 4 q^{82} - 4 q^{83} - 80 q^{84} + 36 q^{85} - 4 q^{86} - 4 q^{88} + 34 q^{90} - 18 q^{91} + 60 q^{92} + 10 q^{93} - 12 q^{94} - 4 q^{95} + 4 q^{96} - 8 q^{97} - 82 q^{98} - 6 q^{99} + O(q^{100}) \)

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.