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Properties

Label 2842.2.bw
Level $2842$
Weight $2$
Character orbit 2842.bw
Rep. character $\chi_{2842}(23,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1680$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2842.bw (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2842, [\chi])\).

Total New Old
Modular forms 5088 1680 3408
Cusp forms 4992 1680 3312
Eisenstein series 96 0 96

Trace form

\( 1680 q + 140 q^{4} + 4 q^{5} - 14 q^{6} + 4 q^{7} + 164 q^{9} + O(q^{10}) \) \( 1680 q + 140 q^{4} + 4 q^{5} - 14 q^{6} + 4 q^{7} + 164 q^{9} - 18 q^{10} - 8 q^{13} - 4 q^{14} - 66 q^{15} + 140 q^{16} - 72 q^{17} - 8 q^{20} - 30 q^{21} + 16 q^{22} + 30 q^{23} - 14 q^{24} + 136 q^{25} - 24 q^{27} + 4 q^{28} + 2 q^{29} - 4 q^{30} + 16 q^{31} + 14 q^{33} - 56 q^{34} + 88 q^{35} - 286 q^{36} + 176 q^{37} - 70 q^{38} - 12 q^{39} - 4 q^{40} + 38 q^{41} - 14 q^{42} - 12 q^{43} + 108 q^{45} - 12 q^{46} + 60 q^{47} + 6 q^{49} + 16 q^{50} - 12 q^{51} + 4 q^{52} - 26 q^{53} - 112 q^{54} - 16 q^{55} + 8 q^{56} + 64 q^{57} - 12 q^{58} + 160 q^{59} - 72 q^{60} - 2 q^{61} - 48 q^{62} + 60 q^{63} - 280 q^{64} + 30 q^{65} - 16 q^{66} - 8 q^{67} - 30 q^{68} + 124 q^{69} - 36 q^{70} + 54 q^{71} + 80 q^{73} - 12 q^{74} + 180 q^{75} + 130 q^{77} - 24 q^{78} - 16 q^{79} + 4 q^{80} + 204 q^{81} + 24 q^{82} - 60 q^{83} - 10 q^{84} + 64 q^{85} - 12 q^{86} + 98 q^{87} - 22 q^{88} + 98 q^{89} - 24 q^{90} - 44 q^{91} + 24 q^{92} + 30 q^{93} + 64 q^{94} + 148 q^{95} - 28 q^{96} + 250 q^{97} + 24 q^{98} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2842, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2842, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2842, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1421, [\chi])\)\(^{\oplus 2}\)