Properties

Label 2736.3.he
Level $2736$
Weight $3$
Character orbit 2736.he
Rep. character $\chi_{2736}(5,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $11472$
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.he (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2736 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 11568 11568 0
Cusp forms 11472 11472 0
Eisenstein series 96 96 0

Trace form

\( 11472q - 18q^{2} - 12q^{3} - 6q^{4} - 18q^{5} - 12q^{6} + O(q^{10}) \) \( 11472q - 18q^{2} - 12q^{3} - 6q^{4} - 18q^{5} - 12q^{6} - 24q^{10} - 6q^{12} - 6q^{13} - 18q^{14} - 24q^{15} - 6q^{16} - 24q^{18} - 24q^{19} - 36q^{20} - 66q^{21} - 6q^{22} - 12q^{24} + 432q^{26} - 6q^{27} + 72q^{28} - 18q^{29} - 594q^{30} - 24q^{31} - 18q^{32} - 24q^{33} - 6q^{34} - 450q^{35} - 12q^{36} - 48q^{37} - 18q^{38} - 6q^{40} - 528q^{42} - 6q^{43} + 594q^{44} - 6q^{45} - 12q^{46} - 36q^{47} - 12q^{48} + 39156q^{49} - 12q^{51} - 6q^{52} + 450q^{54} + 846q^{56} - 12q^{58} - 18q^{59} - 1104q^{60} - 6q^{61} - 72q^{62} - 612q^{63} - 12q^{64} - 1332q^{66} - 6q^{67} - 18q^{68} - 6q^{69} - 594q^{70} + 288q^{72} - 774q^{74} - 696q^{75} - 6q^{76} - 36q^{77} + 12q^{78} - 12q^{79} - 24q^{81} - 24q^{82} - 18q^{83} - 594q^{84} - 6q^{85} - 18q^{86} + 6q^{88} - 552q^{90} + 270q^{91} - 18q^{92} - 120q^{93} - 12q^{94} - 36q^{95} - 942q^{96} - 12q^{97} - 810q^{98} - 984q^{99} + O(q^{100}) \)

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

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