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Properties

Label 2016.2.fm
Level $2016$
Weight $2$
Character orbit 2016.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

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

Display 100 coefficients 10 coefficients

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

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