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Properties

Label 2842.2.bh
Level $2842$
Weight $2$
Character orbit 2842.bh
Rep. character $\chi_{2842}(225,\cdot)$
Character field $\Q(\zeta_{14})$
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.bh (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{14})\)
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

\( 840 q + 140 q^{4} - 4 q^{5} - 10 q^{6} + 4 q^{7} + 148 q^{9} + O(q^{10}) \) \( 840 q + 140 q^{4} - 4 q^{5} - 10 q^{6} + 4 q^{7} + 148 q^{9} + 14 q^{10} - 4 q^{13} - 14 q^{15} - 140 q^{16} - 28 q^{17} - 24 q^{20} - 14 q^{21} + 12 q^{22} - 18 q^{23} - 4 q^{24} - 132 q^{25} - 4 q^{28} - 8 q^{29} - 20 q^{30} - 28 q^{31} + 10 q^{33} + 32 q^{34} + 16 q^{35} - 134 q^{36} + 10 q^{38} - 42 q^{39} + 14 q^{40} - 98 q^{41} - 28 q^{43} - 68 q^{45} - 28 q^{47} - 24 q^{49} + 28 q^{50} + 24 q^{51} - 24 q^{52} + 8 q^{53} + 8 q^{54} + 56 q^{55} - 14 q^{56} + 12 q^{57} - 8 q^{58} + 54 q^{59} - 14 q^{60} + 104 q^{62} - 14 q^{63} + 140 q^{64} - 24 q^{65} + 16 q^{67} + 42 q^{68} - 70 q^{69} - 70 q^{70} + 100 q^{71} + 14 q^{73} + 18 q^{74} - 70 q^{75} - 14 q^{77} - 32 q^{78} - 4 q^{80} - 194 q^{81} - 32 q^{82} - 6 q^{83} - 112 q^{84} - 28 q^{85} - 24 q^{86} - 166 q^{87} - 12 q^{88} + 56 q^{90} - 74 q^{91} - 24 q^{92} - 24 q^{93} - 10 q^{94} + 4 q^{96} + 28 q^{97} + 56 q^{98} + O(q^{100}) \)

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

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