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Properties

Label 2842.2.bx
Level $2842$
Weight $2$
Character orbit 2842.bx
Rep. character $\chi_{2842}(837,\cdot)$
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.bx (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

\( 1680 q + 140 q^{4} + 4 q^{5} - 14 q^{6} + 4 q^{7} + 136 q^{9} + O(q^{10}) \) \( 1680 q + 140 q^{4} + 4 q^{5} - 14 q^{6} + 4 q^{7} + 136 q^{9} - 18 q^{10} - 8 q^{13} - 4 q^{14} - 66 q^{15} + 140 q^{16} + 96 q^{17} + 48 q^{20} - 30 q^{21} - 12 q^{22} - 54 q^{23} + 136 q^{25} - 108 q^{27} + 4 q^{28} + 16 q^{29} + 10 q^{30} + 44 q^{31} + 56 q^{33} - 56 q^{34} + 4 q^{35} - 286 q^{36} - 20 q^{37} + 28 q^{38} - 54 q^{39} - 18 q^{40} - 74 q^{41} - 12 q^{43} - 74 q^{45} - 12 q^{46} + 228 q^{47} - 8 q^{49} - 12 q^{50} - 12 q^{51} - 24 q^{52} - 12 q^{53} - 16 q^{55} - 6 q^{56} - 48 q^{57} - 12 q^{58} - 106 q^{59} + 180 q^{60} - 16 q^{61} + 176 q^{62} - 122 q^{63} - 280 q^{64} - 12 q^{65} - 16 q^{66} - 8 q^{67} + 68 q^{68} + 68 q^{69} - 106 q^{70} + 12 q^{71} - 18 q^{73} + 72 q^{74} - 72 q^{75} - 234 q^{77} + 32 q^{78} - 16 q^{79} + 4 q^{80} + 50 q^{81} - 32 q^{82} - 4 q^{83} - 80 q^{84} + 36 q^{85} - 12 q^{86} - 210 q^{87} + 48 q^{88} - 56 q^{89} - 24 q^{90} + 96 q^{91} + 24 q^{92} - 12 q^{93} - 6 q^{94} - 188 q^{95} - 100 q^{97} - 4 q^{98} + 64 q^{99} + O(q^{100}) \)

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

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