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Properties

Label 2015.2.j
Level $2015$
Weight $2$
Character orbit 2015.j
Rep. character $\chi_{2015}(191,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $300$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 456 300 156
Cusp forms 440 300 140
Eisenstein series 16 0 16

Trace form

\( 300 q - 6 q^{3} - 152 q^{4} + 12 q^{6} - 20 q^{7} + 12 q^{8} - 152 q^{9} + O(q^{10}) \) \( 300 q - 6 q^{3} - 152 q^{4} + 12 q^{6} - 20 q^{7} + 12 q^{8} - 152 q^{9} + 4 q^{11} - 4 q^{12} - 4 q^{13} + 12 q^{14} - 160 q^{16} + 52 q^{17} + 28 q^{18} - 20 q^{19} - 4 q^{20} + 30 q^{21} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 150 q^{25} + 16 q^{26} + 72 q^{27} + 32 q^{28} + 4 q^{29} - 8 q^{30} - 36 q^{31} - 22 q^{32} - 8 q^{33} + 6 q^{34} + 332 q^{36} + 14 q^{37} - 10 q^{38} - 26 q^{39} - 16 q^{41} + 48 q^{42} + 8 q^{44} + 16 q^{45} - 12 q^{46} - 48 q^{47} + 232 q^{49} - 4 q^{51} - 18 q^{52} + 8 q^{53} - 66 q^{54} - 20 q^{55} - 72 q^{56} + 26 q^{57} + 72 q^{59} + 18 q^{61} - 12 q^{62} + 52 q^{63} + 428 q^{64} + 28 q^{66} - 28 q^{67} - 94 q^{68} + 96 q^{69} + 8 q^{70} - 20 q^{71} + 28 q^{72} - 26 q^{73} - 80 q^{74} + 12 q^{75} + 72 q^{76} - 40 q^{77} + 42 q^{78} + 16 q^{80} - 158 q^{81} + 28 q^{82} - 2 q^{83} + 80 q^{84} - 104 q^{86} + 12 q^{87} - 36 q^{88} - 64 q^{89} + 8 q^{90} + 64 q^{91} + 28 q^{92} - 18 q^{93} - 102 q^{94} + 4 q^{95} - 58 q^{96} - 74 q^{97} - 58 q^{98} - 20 q^{99} + O(q^{100}) \)

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

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