Properties

Label 2016.2.fm
Level 2016
Weight 2
Character orbit fm
Rep. character \(\chi_{2016}(115,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 3040
Sturm bound 768

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Defining parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2016.fm (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2016 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2016, [\chi])\).

Total New Old
Modular forms 3104 3104 0
Cusp forms 3040 3040 0
Eisenstein series 64 64 0

Trace form

\( 3040q - 8q^{2} - 12q^{3} - 8q^{4} - 12q^{5} - 4q^{7} - 32q^{8} - 4q^{9} + O(q^{10}) \) \( 3040q - 8q^{2} - 12q^{3} - 8q^{4} - 12q^{5} - 4q^{7} - 32q^{8} - 4q^{9} - 24q^{10} + 4q^{11} - 12q^{12} - 4q^{14} - 32q^{15} - 8q^{16} - 4q^{18} - 24q^{19} - 8q^{21} - 8q^{22} + 4q^{23} - 12q^{24} + 4q^{25} - 24q^{26} - 16q^{28} - 8q^{29} - 52q^{30} - 8q^{32} - 24q^{33} + 24q^{34} - 16q^{35} - 56q^{36} - 8q^{37} - 12q^{38} - 4q^{39} - 12q^{40} + 92q^{42} - 8q^{43} + 36q^{44} - 12q^{45} - 8q^{46} - 8q^{50} + 20q^{51} - 12q^{52} - 8q^{53} - 12q^{54} - 84q^{56} - 16q^{57} + 4q^{58} - 20q^{60} - 32q^{64} - 16q^{65} - 12q^{66} - 8q^{67} - 12q^{68} - 4q^{70} - 32q^{71} - 4q^{72} - 24q^{73} + 4q^{74} - 12q^{75} - 4q^{77} + 60q^{78} - 16q^{79} - 24q^{80} - 24q^{82} - 120q^{83} + 180q^{84} + 12q^{85} + 4q^{86} - 12q^{87} + 4q^{88} - 24q^{89} - 216q^{90} - 16q^{91} - 8q^{92} - 52q^{93} - 12q^{96} + 60q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database