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Properties

Label 2873.2.e
Level $2873$
Weight $2$
Character orbit 2873.e
Rep. character $\chi_{2873}(698,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $412$
Sturm bound $546$

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Defining parameters

Level: \( N \) \(=\) \( 2873 = 13^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2873.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(546\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2873, [\chi])\).

Total New Old
Modular forms 572 412 160
Cusp forms 516 412 104
Eisenstein series 56 0 56

Trace form

\( 412 q + 2 q^{3} - 208 q^{4} - 6 q^{6} + 2 q^{7} + 12 q^{8} - 208 q^{9} + O(q^{10}) \) \( 412 q + 2 q^{3} - 208 q^{4} - 6 q^{6} + 2 q^{7} + 12 q^{8} - 208 q^{9} + 20 q^{10} - 4 q^{11} - 28 q^{12} - 8 q^{14} + 14 q^{15} - 196 q^{16} + 4 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} + 10 q^{22} + 8 q^{23} - 28 q^{24} + 408 q^{25} + 20 q^{27} + 12 q^{28} + 14 q^{29} - 20 q^{30} - 12 q^{31} - 22 q^{32} - 4 q^{33} - 12 q^{35} - 198 q^{36} + 18 q^{37} - 48 q^{38} - 60 q^{40} + 18 q^{41} + 16 q^{42} + 24 q^{43} + 56 q^{44} + 14 q^{45} - 12 q^{46} - 4 q^{47} + 80 q^{48} - 236 q^{49} - 36 q^{50} - 16 q^{51} + 24 q^{53} + 2 q^{54} + 16 q^{55} + 34 q^{56} + 12 q^{57} + 8 q^{58} + 34 q^{59} - 112 q^{60} + 2 q^{61} - 30 q^{63} + 460 q^{64} - 200 q^{66} - 10 q^{67} + 12 q^{68} + 30 q^{69} - 68 q^{70} - 30 q^{71} - 30 q^{72} + 32 q^{73} + 32 q^{74} + 78 q^{75} - 10 q^{76} - 28 q^{77} - 56 q^{79} + 54 q^{80} - 178 q^{81} + 42 q^{82} - 24 q^{83} + 36 q^{84} - 2 q^{85} + 104 q^{86} + 2 q^{87} + 44 q^{88} - 18 q^{89} - 44 q^{90} - 136 q^{92} + 8 q^{93} + 62 q^{94} + 88 q^{95} + 56 q^{96} - 24 q^{97} - 8 q^{98} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2873, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2873, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2873, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(221, [\chi])\)\(^{\oplus 2}\)