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Properties

Label 2842.2.bf
Level $2842$
Weight $2$
Character orbit 2842.bf
Rep. character $\chi_{2842}(295,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $612$
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.bf (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
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 2616 612 2004
Cusp forms 2424 612 1812
Eisenstein series 192 0 192

Trace form

\( 612 q + 102 q^{4} + 2 q^{5} + 12 q^{6} + 104 q^{9} + O(q^{10}) \) \( 612 q + 102 q^{4} + 2 q^{5} + 12 q^{6} + 104 q^{9} - 22 q^{13} + 14 q^{15} - 102 q^{16} - 2 q^{20} - 8 q^{22} + 28 q^{23} - 12 q^{24} - 98 q^{25} + 14 q^{26} + 84 q^{27} - 14 q^{29} + 8 q^{30} - 28 q^{31} + 50 q^{33} + 20 q^{34} - 118 q^{36} + 56 q^{37} - 2 q^{38} - 28 q^{39} - 14 q^{40} - 28 q^{43} + 28 q^{44} - 48 q^{45} + 42 q^{47} + 28 q^{50} - 84 q^{51} - 6 q^{52} + 82 q^{53} - 40 q^{54} - 84 q^{55} + 92 q^{57} - 22 q^{58} + 80 q^{59} + 14 q^{60} - 28 q^{61} + 18 q^{62} + 102 q^{64} + 142 q^{65} - 16 q^{67} + 14 q^{68} - 84 q^{69} - 18 q^{71} + 42 q^{73} - 34 q^{74} + 28 q^{76} - 112 q^{78} + 28 q^{79} + 2 q^{80} - 50 q^{81} + 12 q^{82} + 20 q^{83} - 140 q^{85} + 76 q^{86} + 44 q^{87} - 20 q^{88} + 14 q^{89} + 70 q^{90} - 28 q^{92} + 10 q^{93} + 44 q^{94} - 2 q^{96} - 28 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2842, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(203, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(406, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1421, [\chi])\)\(^{\oplus 2}\)