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Properties

Label 2842.2.k
Level $2842$
Weight $2$
Character orbit 2842.k
Rep. character $\chi_{2842}(1205,\cdot)$
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.k (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

\( 840 q - 140 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 148 q^{9} + O(q^{10}) \) \( 840 q - 140 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 148 q^{9} - 8 q^{10} - 4 q^{13} + 6 q^{14} - 18 q^{15} - 140 q^{16} - 32 q^{17} - 4 q^{20} - 32 q^{21} - 16 q^{22} + 18 q^{23} + 16 q^{24} - 148 q^{25} - 6 q^{27} + 10 q^{28} - 2 q^{29} - 8 q^{30} - 10 q^{31} + 16 q^{33} + 32 q^{34} - 40 q^{35} - 134 q^{36} + 2 q^{37} - 22 q^{38} - 24 q^{39} - 8 q^{40} - 16 q^{41} - 24 q^{42} + 12 q^{43} - 30 q^{45} + 18 q^{46} + 6 q^{47} + 26 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 24 q^{53} - 16 q^{54} + 6 q^{55} - 8 q^{56} + 6 q^{57} - 24 q^{58} - 44 q^{59} - 18 q^{60} + 80 q^{61} - 24 q^{62} - 46 q^{63} - 140 q^{64} + 18 q^{65} + 80 q^{66} + 12 q^{67} - 32 q^{68} + 26 q^{69} + 44 q^{70} + 58 q^{71} - 18 q^{73} - 24 q^{74} - 88 q^{75} - 34 q^{77} + 24 q^{78} + 80 q^{79} - 4 q^{80} - 82 q^{81} - 24 q^{82} - 26 q^{83} + 24 q^{84} + 20 q^{85} + 18 q^{86} - 48 q^{87} - 16 q^{88} - 28 q^{89} - 32 q^{90} + 26 q^{91} - 24 q^{92} - 24 q^{93} + 92 q^{94} - 40 q^{95} + 2 q^{96} - 30 q^{97} - 20 q^{98} - 64 q^{99} + O(q^{100}) \)

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

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