↑

Properties

Label 2015.2.gr
Level $2015$
Weight $2$
Character orbit 2015.gr
Rep. character $\chi_{2015}(17,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3520$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.gr (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

\( 3520 q - 18 q^{2} - 10 q^{3} - 48 q^{6} - 24 q^{7} + O(q^{10}) \) \( 3520 q - 18 q^{2} - 10 q^{3} - 48 q^{6} - 24 q^{7} - 12 q^{10} - 48 q^{11} - 18 q^{12} - 14 q^{13} - 30 q^{15} - 420 q^{16} - 4 q^{17} + 42 q^{18} + 90 q^{20} - 96 q^{21} + 40 q^{22} + 2 q^{23} - 16 q^{25} - 48 q^{26} + 20 q^{27} - 30 q^{28} + 120 q^{30} + 30 q^{32} + 18 q^{33} + 12 q^{35} - 1616 q^{36} - 48 q^{37} - 76 q^{38} - 18 q^{40} - 72 q^{41} + 140 q^{42} + 8 q^{43} + 6 q^{45} - 156 q^{46} - 4 q^{48} - 180 q^{50} - 64 q^{51} + 120 q^{52} - 48 q^{53} - 110 q^{55} + 80 q^{56} - 30 q^{58} + 108 q^{60} - 48 q^{61} - 34 q^{62} + 102 q^{63} - 142 q^{65} - 112 q^{66} - 48 q^{67} - 60 q^{71} - 30 q^{72} - 50 q^{75} - 540 q^{76} + 60 q^{77} + 68 q^{78} - 54 q^{80} + 676 q^{81} + 10 q^{82} - 102 q^{83} - 126 q^{85} + 16 q^{87} + 48 q^{88} - 156 q^{90} - 96 q^{91} - 78 q^{93} - 194 q^{95} + 240 q^{96} + 198 q^{97} + O(q^{100}) \)

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.