Properties

Label 2736.3.du
Level $2736$
Weight $3$
Character orbit 2736.du
Rep. character $\chi_{2736}(619,\cdot)$
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.du (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

\( 3824q + 2q^{2} - 2q^{3} + 2q^{4} - 4q^{5} - 2q^{6} - 8q^{7} - 16q^{8} + O(q^{10}) \) \( 3824q + 2q^{2} - 2q^{3} + 2q^{4} - 4q^{5} - 2q^{6} - 8q^{7} - 16q^{8} - 4q^{10} - 4q^{11} - 8q^{12} + 2q^{13} + 28q^{14} + 2q^{16} - 8q^{17} - 8q^{19} + 38q^{20} + 34q^{21} - 4q^{22} + 4q^{23} - 18q^{24} - 112q^{26} - 8q^{27} + 28q^{28} - 4q^{29} - 196q^{30} + 2q^{32} - 4q^{33} + 28q^{34} + 46q^{35} - 66q^{36} - 16q^{37} - 254q^{38} - 16q^{39} - 4q^{40} + 26q^{42} + 2q^{43} - 70q^{44} + 42q^{45} - 200q^{46} - 562q^{48} - 13056q^{49} + 12q^{50} + 34q^{51} + 2q^{52} - 4q^{53} + 306q^{54} - 8q^{55} - 560q^{56} - 4q^{58} - 4q^{59} + 298q^{60} - 4q^{61} + 780q^{62} - 16q^{64} - 8q^{65} - 634q^{66} + 2q^{67} + 28q^{68} - 26q^{69} - 200q^{70} - 8q^{71} + 154q^{72} - 82q^{74} - 388q^{75} - 314q^{76} + 388q^{77} + 14q^{78} + 236q^{80} - 4q^{81} + 12q^{82} - 4q^{83} - 384q^{84} - 98q^{85} + 2q^{86} + 432q^{87} - 4q^{88} - 146q^{90} + 94q^{91} + 130q^{92} + 16q^{93} + 12q^{94} + 836q^{96} + 4q^{97} - 102q^{98} - 96q^{99} + O(q^{100}) \)

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

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