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Properties

Label 2015.2.ex
Level $2015$
Weight $2$
Character orbit 2015.ex
Rep. character $\chi_{2015}(121,\cdot)$
Character field $\Q(\zeta_{30})$
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.ex (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1200 q + 12 q^{3} - 152 q^{4} + 18 q^{6} - 18 q^{7} + 90 q^{8} - 304 q^{9} + O(q^{10}) \) \( 1200 q + 12 q^{3} - 152 q^{4} + 18 q^{6} - 18 q^{7} + 90 q^{8} - 304 q^{9} - 6 q^{11} - 2 q^{12} - 6 q^{13} - 32 q^{14} + 152 q^{16} + 30 q^{17} + 48 q^{18} + 18 q^{19} - 68 q^{21} + 24 q^{22} + 10 q^{23} + 600 q^{25} + 28 q^{26} + 72 q^{27} - 40 q^{28} - 4 q^{29} - 32 q^{30} + 4 q^{31} + 156 q^{32} + 24 q^{33} - 30 q^{34} + 646 q^{36} + 30 q^{38} - 8 q^{39} + 12 q^{41} - 24 q^{42} - 58 q^{43} + 24 q^{44} - 72 q^{46} + 12 q^{48} - 164 q^{49} + 4 q^{51} - 114 q^{52} - 48 q^{53} + 54 q^{54} + 20 q^{55} + 20 q^{56} - 174 q^{57} - 12 q^{58} - 60 q^{59} - 6 q^{61} + 10 q^{62} - 264 q^{63} + 294 q^{64} - 32 q^{66} + 90 q^{67} - 340 q^{68} + 276 q^{69} + 18 q^{73} + 100 q^{74} + 6 q^{75} + 40 q^{76} - 16 q^{77} + 116 q^{78} - 76 q^{79} - 24 q^{80} - 188 q^{81} - 76 q^{82} + 6 q^{83} + 12 q^{86} + 66 q^{87} - 34 q^{88} + 48 q^{90} + 100 q^{91} - 532 q^{92} + 74 q^{93} - 86 q^{94} + 4 q^{95} + 246 q^{96} - 70 q^{97} - 150 q^{99} + O(q^{100}) \)

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

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