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Properties

Label 2016.3.fr
Level $2016$
Weight $3$
Character orbit 2016.fr
Rep. character $\chi_{2016}(59,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $6112$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2016.fr (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2016 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2016, [\chi])\).

Total New Old
Modular forms 6176 6176 0
Cusp forms 6112 6112 0
Eisenstein series 64 64 0

Trace form

\( 6112 q - 12 q^{2} - 12 q^{3} + 4 q^{4} - 24 q^{5} - 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 6112 q - 12 q^{2} - 12 q^{3} + 4 q^{4} - 24 q^{5} - 4 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 12 q^{14} - 32 q^{15} + 4 q^{16} - 4 q^{18} - 24 q^{19} - 8 q^{21} - 8 q^{22} - 12 q^{24} - 8 q^{25} - 16 q^{28} - 24 q^{29} + 44 q^{30} - 12 q^{32} - 24 q^{33} + 48 q^{34} + 184 q^{36} - 8 q^{37} - 24 q^{38} - 4 q^{39} - 28 q^{42} - 8 q^{43} + 396 q^{44} - 12 q^{45} - 8 q^{46} - 24 q^{47} - 24 q^{50} - 76 q^{51} - 12 q^{54} - 12 q^{56} - 16 q^{57} - 8 q^{58} - 12 q^{59} + 124 q^{60} - 12 q^{61} + 96 q^{62} - 32 q^{64} - 24 q^{65} - 12 q^{66} + 4 q^{67} - 24 q^{68} - 4 q^{70} - 4 q^{72} - 24 q^{73} - 312 q^{75} - 12 q^{77} + 60 q^{78} + 8 q^{79} - 24 q^{82} - 1440 q^{83} + 228 q^{84} - 108 q^{85} - 12 q^{87} - 8 q^{88} - 1080 q^{90} - 16 q^{91} - 24 q^{92} + 68 q^{93} - 12 q^{94} - 216 q^{96} + 660 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

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