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Properties

Label 3015.2.el
Level $3015$
Weight $2$
Character orbit 3015.el
Rep. character $\chi_{3015}(23,\cdot)$
Character field $\Q(\zeta_{132})$
Dimension $16160$
Sturm bound $816$

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Defining parameters

Level: \( N \) \(=\) \( 3015 = 3^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3015.el (of order \(132\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3015 \)
Character field: \(\Q(\zeta_{132})\)
Sturm bound: \(816\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3015, [\chi])\).

Total New Old
Modular forms 16480 16480 0
Cusp forms 16160 16160 0
Eisenstein series 320 320 0

Trace form

\( 16160 q - 60 q^{2} - 32 q^{3} - 54 q^{5} - 88 q^{6} - 18 q^{7} + O(q^{10}) \) \( 16160 q - 60 q^{2} - 32 q^{3} - 54 q^{5} - 88 q^{6} - 18 q^{7} - 84 q^{10} - 132 q^{11} + 10 q^{12} - 18 q^{13} - 44 q^{15} - 832 q^{16} - 50 q^{18} - 66 q^{20} - 200 q^{21} - 26 q^{22} - 66 q^{23} - 12 q^{25} - 48 q^{26} - 68 q^{27} - 104 q^{28} - 70 q^{30} - 48 q^{31} - 96 q^{32} - 30 q^{33} - 24 q^{36} - 46 q^{37} - 10 q^{40} - 132 q^{41} - 32 q^{42} - 18 q^{43} - 92 q^{45} - 180 q^{46} - 66 q^{47} + 174 q^{48} - 66 q^{50} - 36 q^{51} - 30 q^{52} + 52 q^{55} - 132 q^{56} - 26 q^{57} - 186 q^{58} + 118 q^{60} + 60 q^{61} - 28 q^{63} - 60 q^{65} - 392 q^{66} - 26 q^{67} - 144 q^{68} - 58 q^{70} + 120 q^{71} + 316 q^{72} - 84 q^{73} + 154 q^{75} - 20 q^{76} - 66 q^{77} + 114 q^{78} + 18 q^{80} - 140 q^{81} - 80 q^{82} - 180 q^{83} - 18 q^{85} - 132 q^{86} - 204 q^{87} - 34 q^{88} - 32 q^{90} - 144 q^{91} - 66 q^{92} - 320 q^{93} - 66 q^{95} + 152 q^{96} + 26 q^{97} - 66 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3015, [\chi])\) into newform subspaces

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