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Properties

Label 2873.2.m
Level $2873$
Weight $2$
Character orbit 2873.m
Rep. character $\chi_{2873}(868,\cdot)$
Character field $\Q(\zeta_{6})$
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.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(546\)

Dimensions

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

Total New Old
Modular forms 576 412 164
Cusp forms 520 412 108
Eisenstein series 56 0 56

Trace form

\( 412 q - 2 q^{3} + 208 q^{4} + 18 q^{6} + 6 q^{7} - 208 q^{9} + O(q^{10}) \) \( 412 q - 2 q^{3} + 208 q^{4} + 18 q^{6} + 6 q^{7} - 208 q^{9} - 12 q^{10} + 12 q^{11} + 12 q^{12} + 8 q^{14} - 6 q^{15} - 196 q^{16} + 4 q^{17} - 6 q^{19} + 2 q^{22} + 8 q^{23} - 12 q^{24} - 400 q^{25} + 4 q^{27} + 12 q^{28} + 2 q^{29} - 28 q^{30} - 66 q^{32} + 12 q^{33} + 186 q^{36} - 6 q^{37} + 96 q^{38} - 52 q^{40} + 18 q^{41} + 64 q^{42} - 52 q^{43} - 30 q^{45} - 60 q^{46} + 40 q^{48} + 208 q^{49} - 48 q^{50} - 16 q^{51} - 16 q^{53} - 90 q^{54} + 20 q^{55} - 46 q^{56} + 84 q^{58} - 18 q^{59} - 10 q^{61} + 36 q^{62} + 30 q^{63} - 388 q^{64} - 136 q^{66} + 42 q^{67} - 12 q^{68} - 6 q^{69} - 30 q^{71} + 18 q^{72} + 24 q^{74} - 50 q^{75} - 42 q^{76} + 28 q^{77} - 40 q^{79} - 66 q^{80} - 122 q^{81} + 14 q^{82} + 96 q^{84} + 6 q^{85} + 38 q^{87} - 68 q^{88} + 42 q^{89} + 116 q^{90} + 16 q^{92} - 48 q^{93} + 26 q^{94} - 56 q^{95} + 36 q^{97} + 24 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2873, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)