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Properties

Label 3015.2.cs
Level $3015$
Weight $2$
Character orbit 3015.cs
Rep. character $\chi_{3015}(181,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $2280$
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.cs (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(816\)

Dimensions

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

Total New Old
Modular forms 8320 2280 6040
Cusp forms 8000 2280 5720
Eisenstein series 320 0 320

Trace form

\( 2280 q + 2 q^{2} + 120 q^{4} + 4 q^{5} - 2 q^{7} - 12 q^{8} + O(q^{10}) \) \( 2280 q + 2 q^{2} + 120 q^{4} + 4 q^{5} - 2 q^{7} - 12 q^{8} - 10 q^{11} + 6 q^{13} - 4 q^{14} + 132 q^{16} + 68 q^{17} - 10 q^{19} - 6 q^{20} - 78 q^{22} + 2 q^{23} - 228 q^{25} + 8 q^{26} - 14 q^{28} - 22 q^{29} + 32 q^{31} + 14 q^{32} - 26 q^{34} - 2 q^{35} - 38 q^{37} + 130 q^{38} - 24 q^{41} - 28 q^{43} - 24 q^{44} - 20 q^{46} + 26 q^{47} + 64 q^{49} + 2 q^{50} + 76 q^{52} + 140 q^{53} - 4 q^{55} - 38 q^{56} - 160 q^{58} + 96 q^{59} - 80 q^{61} + 8 q^{62} - 224 q^{64} + 4 q^{65} - 126 q^{67} + 196 q^{68} - 62 q^{70} - 20 q^{71} + 332 q^{73} + 80 q^{74} + 68 q^{76} + 60 q^{77} - 88 q^{79} - 14 q^{80} + 100 q^{82} + 64 q^{83} + 2 q^{85} - 36 q^{86} + 322 q^{88} + 132 q^{89} + 184 q^{91} - 96 q^{92} - 24 q^{95} - 70 q^{97} - 144 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3015, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3015, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(603, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 2}\)