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Properties

Label 2015.2.gu
Level $2015$
Weight $2$
Character orbit 2015.gu
Rep. character $\chi_{2015}(42,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3520$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.gu (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2015, [\chi])\).

Total New Old
Modular forms 3648 3648 0
Cusp forms 3520 3520 0
Eisenstein series 128 128 0

Trace form

\( 3520 q - 6 q^{2} - 10 q^{3} - 16 q^{5} - 48 q^{6} - 12 q^{7} - 8 q^{8} + O(q^{10}) \) \( 3520 q - 6 q^{2} - 10 q^{3} - 16 q^{5} - 48 q^{6} - 12 q^{7} - 8 q^{8} - 12 q^{10} - 8 q^{11} - 2 q^{12} - 14 q^{13} - 10 q^{15} - 436 q^{16} - 4 q^{17} - 14 q^{18} - 102 q^{20} - 40 q^{21} + 40 q^{22} - 22 q^{23} - 16 q^{25} - 48 q^{26} + 20 q^{27} + 18 q^{28} - 120 q^{30} - 96 q^{31} - 38 q^{32} + 90 q^{33} + 1584 q^{36} - 68 q^{38} - 38 q^{40} - 16 q^{41} - 76 q^{42} - 16 q^{43} - 2 q^{45} - 4 q^{46} - 32 q^{47} - 124 q^{48} + 60 q^{50} - 64 q^{51} + 80 q^{52} - 48 q^{53} + 90 q^{55} + 16 q^{56} - 48 q^{57} - 10 q^{58} + 20 q^{60} + 48 q^{61} - 86 q^{62} + 18 q^{63} - 106 q^{65} + 32 q^{66} + 16 q^{67} - 96 q^{70} + 180 q^{71} - 54 q^{72} - 28 q^{73} - 98 q^{75} - 44 q^{76} - 60 q^{77} - 60 q^{78} + 98 q^{80} + 740 q^{81} - 22 q^{82} - 266 q^{83} - 98 q^{85} - 104 q^{86} - 24 q^{87} + 12 q^{90} - 96 q^{91} + 30 q^{93} + 182 q^{95} + 40 q^{96} + 90 q^{97} + 56 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces

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