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Properties

Label 2015.2.ef
Level $2015$
Weight $2$
Character orbit 2015.ef
Rep. character $\chi_{2015}(386,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1200$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.ef (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1824 1200 624
Cusp forms 1760 1200 560
Eisenstein series 64 0 64

Trace form

\( 1200 q - 12 q^{3} + 152 q^{4} + 6 q^{6} - 10 q^{7} + 18 q^{8} - 304 q^{9} + O(q^{10}) \) \( 1200 q - 12 q^{3} + 152 q^{4} + 6 q^{6} - 10 q^{7} + 18 q^{8} - 304 q^{9} - 18 q^{11} + 34 q^{12} + 30 q^{13} - 32 q^{14} + 160 q^{16} + 6 q^{17} - 28 q^{18} - 10 q^{19} - 8 q^{20} + 20 q^{21} - 8 q^{22} + 22 q^{23} - 24 q^{24} - 600 q^{25} + 28 q^{26} - 72 q^{27} - 96 q^{28} - 4 q^{29} - 32 q^{30} - 4 q^{31} - 28 q^{32} + 8 q^{33} + 34 q^{34} - 634 q^{36} + 28 q^{37} - 30 q^{38} + 56 q^{39} - 28 q^{41} + 24 q^{42} - 90 q^{43} + 12 q^{44} + 8 q^{45} + 32 q^{46} + 48 q^{47} - 60 q^{48} + 96 q^{49} + 4 q^{51} - 162 q^{52} - 8 q^{53} + 66 q^{54} - 20 q^{55} - 36 q^{56} - 86 q^{57} + 360 q^{58} + 76 q^{59} - 18 q^{61} + 18 q^{62} + 28 q^{63} - 218 q^{64} + 32 q^{66} - 14 q^{67} + 292 q^{68} - 132 q^{69} - 8 q^{70} + 120 q^{71} + 56 q^{72} + 26 q^{73} - 140 q^{74} + 6 q^{75} - 16 q^{76} + 80 q^{77} - 192 q^{78} + 140 q^{79} - 72 q^{80} - 316 q^{81} - 4 q^{82} + 2 q^{83} - 80 q^{84} - 36 q^{86} + 86 q^{87} - 138 q^{88} - 156 q^{89} - 48 q^{90} + 96 q^{91} + 332 q^{92} + 14 q^{93} + 102 q^{94} - 4 q^{95} - 82 q^{96} - 146 q^{97} + 204 q^{98} - 30 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2015, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)