Properties

Label 2736.3.ej
Level $2736$
Weight $3$
Character orbit 2736.ej
Rep. character $\chi_{2736}(653,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $3824$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.ej (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2736 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 3856 3856 0
Cusp forms 3824 3824 0
Eisenstein series 32 32 0

Trace form

\( 3824q - 6q^{2} - 2q^{3} + 2q^{4} - 2q^{6} + O(q^{10}) \) \( 3824q - 6q^{2} - 2q^{3} + 2q^{4} - 2q^{6} - 4q^{10} - 12q^{11} - 8q^{12} + 2q^{13} - 4q^{15} + 2q^{16} - 16q^{18} - 8q^{19} - 138q^{20} - 38q^{21} - 4q^{22} - 18q^{24} - 8q^{27} - 36q^{28} - 196q^{30} - 8q^{31} - 6q^{32} - 4q^{33} - 36q^{34} - 150q^{35} - 66q^{36} - 16q^{37} - 6q^{38} - 4q^{40} + 170q^{42} + 2q^{43} - 198q^{44} - 58q^{45} + 136q^{46} + 558q^{48} + 13040q^{49} - 12q^{50} - 38q^{51} + 2q^{52} + 306q^{54} - 600q^{56} - 4q^{58} + 426q^{60} - 4q^{61} - 24q^{62} + 192q^{63} - 16q^{64} - 24q^{65} + 630q^{66} + 2q^{67} - 108q^{68} - 26q^{69} + 192q^{70} - 102q^{72} + 246q^{74} + 508q^{75} + 310q^{76} - 12q^{77} + 14q^{78} + 4q^{79} - 720q^{80} - 4q^{81} - 20q^{82} - 12q^{83} - 776q^{84} + 102q^{85} - 6q^{86} - 4q^{88} - 146q^{90} - 102q^{91} - 6q^{92} - 20q^{93} + 12q^{94} - 12q^{95} - 716q^{96} + 4q^{97} - 930q^{98} - 420q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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