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Properties

Label 2842.2.r
Level $2842$
Weight $2$
Character orbit 2842.r
Rep. character $\chi_{2842}(141,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $840$
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.r (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 2544 840 1704
Cusp forms 2496 840 1656
Eisenstein series 48 0 48

Trace form

\( 840 q - 140 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} + 832 q^{9} + O(q^{10}) \) \( 840 q - 140 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} + 832 q^{9} - 8 q^{10} + 24 q^{13} + 6 q^{14} - 18 q^{15} - 140 q^{16} + 24 q^{17} - 4 q^{20} + 24 q^{21} + 12 q^{22} + 18 q^{23} - 12 q^{24} - 134 q^{25} - 48 q^{27} - 4 q^{28} - 2 q^{29} - 8 q^{30} - 10 q^{31} + 16 q^{33} - 24 q^{34} + 2 q^{35} - 134 q^{36} - 40 q^{37} - 22 q^{38} + 60 q^{39} - 8 q^{40} - 2 q^{41} - 24 q^{42} + 12 q^{43} - 2 q^{45} - 24 q^{46} - 8 q^{47} - 44 q^{49} - 16 q^{50} + 18 q^{51} - 4 q^{52} - 24 q^{53} - 16 q^{54} - 8 q^{55} + 20 q^{56} - 64 q^{57} - 24 q^{58} + 26 q^{59} - 18 q^{60} - 32 q^{61} - 10 q^{62} - 88 q^{63} - 140 q^{64} - 24 q^{65} + 80 q^{66} - 16 q^{67} + 24 q^{68} - 16 q^{69} - 12 q^{70} + 2 q^{71} - 18 q^{73} - 24 q^{74} + 24 q^{75} - 104 q^{77} - 32 q^{78} - 32 q^{79} - 4 q^{80} + 744 q^{81} - 24 q^{82} + 2 q^{83} + 24 q^{84} + 48 q^{85} + 18 q^{86} + 78 q^{87} - 2 q^{88} - 56 q^{89} - 32 q^{90} - 72 q^{91} - 24 q^{92} - 24 q^{93} - 6 q^{94} - 12 q^{95} + 2 q^{96} + 110 q^{97} - 20 q^{98} + 20 q^{99} + O(q^{100}) \)

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

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