Properties

Label 2016.2.fk
Level 2016
Weight 2
Character orbit fk
Rep. character \(\chi_{2016}(347,\cdot)\)
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.fk (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

\( 3040q - 12q^{2} - 4q^{3} + 4q^{4} - 16q^{6} - 4q^{7} - 4q^{9} + O(q^{10}) \) \( 3040q - 12q^{2} - 4q^{3} + 4q^{4} - 16q^{6} - 4q^{7} - 4q^{9} - 8q^{10} - 4q^{12} - 8q^{13} - 12q^{14} - 32q^{15} + 4q^{16} - 4q^{18} - 8q^{19} - 24q^{20} - 8q^{21} - 8q^{22} - 44q^{24} - 8q^{25} - 16q^{27} - 16q^{28} - 24q^{29} + 60q^{30} - 12q^{32} - 8q^{33} - 56q^{36} - 8q^{37} - 4q^{39} - 8q^{40} - 24q^{41} - 68q^{42} - 8q^{43} + 132q^{44} - 4q^{45} - 8q^{46} - 24q^{47} - 16q^{48} - 24q^{50} + 20q^{51} - 8q^{52} + 172q^{54} - 32q^{55} - 12q^{56} - 16q^{57} - 8q^{58} - 12q^{59} + 28q^{60} + 4q^{61} - 32q^{64} - 24q^{65} - 20q^{66} + 4q^{67} - 16q^{69} - 4q^{70} - 4q^{72} - 8q^{73} + 16q^{75} - 8q^{76} - 12q^{77} - 92q^{78} + 8q^{79} - 8q^{82} + 96q^{83} + 124q^{84} + 12q^{85} - 4q^{87} - 8q^{88} - 88q^{90} - 16q^{91} - 24q^{92} - 28q^{93} - 28q^{94} - 72q^{96} - 16q^{97} - 180q^{98} - 16q^{99} + O(q^{100}) \)

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