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Properties

Label 2015.2.gi
Level $2015$
Weight $2$
Character orbit 2015.gi
Rep. character $\chi_{2015}(141,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2400$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.gi (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
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 2400 1248
Cusp forms 3520 2400 1120
Eisenstein series 128 0 128

Trace form

\( 2400 q + 36 q^{6} - 20 q^{7} + 72 q^{8} - 304 q^{9} + O(q^{10}) \) \( 2400 q + 36 q^{6} - 20 q^{7} + 72 q^{8} - 304 q^{9} + 8 q^{11} - 16 q^{12} + 20 q^{13} - 64 q^{14} - 312 q^{16} + 24 q^{17} + 52 q^{18} + 20 q^{19} - 8 q^{20} - 200 q^{21} - 24 q^{22} + 80 q^{28} + 24 q^{29} - 8 q^{31} - 128 q^{32} - 32 q^{33} - 72 q^{34} + 68 q^{37} - 92 q^{39} + 4 q^{41} - 192 q^{43} - 20 q^{44} - 16 q^{45} - 88 q^{46} + 48 q^{47} - 24 q^{51} + 224 q^{52} + 72 q^{53} - 376 q^{57} - 96 q^{58} - 40 q^{59} - 72 q^{61} - 96 q^{62} + 20 q^{63} - 540 q^{64} + 48 q^{66} + 60 q^{67} + 72 q^{68} - 360 q^{69} + 8 q^{70} + 96 q^{71} - 44 q^{72} - 88 q^{73} + 8 q^{75} + 240 q^{76} + 76 q^{78} - 32 q^{79} - 96 q^{80} + 588 q^{81} + 120 q^{82} - 12 q^{83} - 128 q^{84} - 168 q^{86} - 304 q^{87} + 120 q^{88} + 268 q^{89} - 48 q^{91} - 128 q^{93} + 16 q^{94} - 152 q^{96} + 128 q^{97} - 180 q^{98} - 240 q^{99} + O(q^{100}) \)

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

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