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Properties

Label 2842.2.bt
Level $2842$
Weight $2$
Character orbit 2842.bt
Rep. character $\chi_{2842}(401,\cdot)$
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.bt (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

\( 1680 q + 140 q^{4} - 24 q^{5} + 28 q^{6} - 10 q^{7} + 136 q^{9} + O(q^{10}) \) \( 1680 q + 140 q^{4} - 24 q^{5} + 28 q^{6} - 10 q^{7} + 136 q^{9} + 24 q^{10} - 8 q^{13} + 10 q^{14} + 18 q^{15} + 140 q^{16} + 96 q^{17} - 8 q^{20} + 68 q^{21} + 16 q^{22} - 54 q^{23} - 844 q^{25} + 60 q^{27} + 4 q^{28} + 16 q^{29} + 10 q^{30} - 40 q^{31} - 14 q^{33} + 60 q^{35} + 1660 q^{36} - 76 q^{37} + 56 q^{38} - 12 q^{39} - 4 q^{40} - 74 q^{41} - 14 q^{42} + 16 q^{43} + 80 q^{45} - 12 q^{46} + 18 q^{47} - 64 q^{49} - 12 q^{50} + 30 q^{51} + 4 q^{52} + 2 q^{53} + 28 q^{54} - 72 q^{55} - 6 q^{56} - 48 q^{57} + 72 q^{58} - 106 q^{59} + 12 q^{60} + 152 q^{61} - 20 q^{62} + 46 q^{63} - 280 q^{64} + 72 q^{65} - 16 q^{66} - 8 q^{67} - 58 q^{68} - 72 q^{69} - 106 q^{70} - 100 q^{71} + 66 q^{73} - 12 q^{74} - 72 q^{75} + 18 q^{77} + 32 q^{78} - 16 q^{79} + 4 q^{80} + 316 q^{81} - 4 q^{82} + 80 q^{83} - 10 q^{84} + 64 q^{85} - 12 q^{86} + 48 q^{88} + 112 q^{89} - 24 q^{90} - 30 q^{91} - 18 q^{92} - 12 q^{93} + 22 q^{94} - 34 q^{95} + 28 q^{96} - 100 q^{97} - 32 q^{98} + 64 q^{99} + O(q^{100}) \)

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

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