↑

Properties

Label 2842.2.bq
Level $2842$
Weight $2$
Character orbit 2842.bq
Rep. character $\chi_{2842}(323,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $840$
Sturm bound $840$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2842.bq (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

\( 840 q + 140 q^{4} + 24 q^{5} + 4 q^{6} - 10 q^{7} + 148 q^{9} + O(q^{10}) \) \( 840 q + 140 q^{4} + 24 q^{5} + 4 q^{6} - 10 q^{7} + 148 q^{9} - 14 q^{10} - 4 q^{13} + 28 q^{14} - 14 q^{15} - 140 q^{16} + 28 q^{17} + 4 q^{20} + 42 q^{21} - 16 q^{22} - 18 q^{23} - 4 q^{24} + 848 q^{25} + 42 q^{27} - 4 q^{28} - 8 q^{29} - 20 q^{30} - 28 q^{31} - 18 q^{33} - 24 q^{34} - 54 q^{35} + 860 q^{36} - 46 q^{38} + 98 q^{41} - 14 q^{42} + 2 q^{45} + 14 q^{47} + 4 q^{49} + 28 q^{50} - 60 q^{51} + 4 q^{52} + 36 q^{53} - 62 q^{54} + 70 q^{55} + 14 q^{56} + 12 q^{57} + 20 q^{58} + 54 q^{59} - 14 q^{60} - 22 q^{62} + 140 q^{64} + 18 q^{65} + 16 q^{67} + 42 q^{68} + 70 q^{70} + 16 q^{71} - 56 q^{73} - 24 q^{74} + 70 q^{75} + 14 q^{77} - 32 q^{78} - 4 q^{80} - 124 q^{81} - 4 q^{82} - 48 q^{83} - 42 q^{84} - 24 q^{86} + 44 q^{87} - 12 q^{88} + 70 q^{89} - 56 q^{90} + 10 q^{91} + 18 q^{92} - 24 q^{93} + 46 q^{94} - 252 q^{95} - 10 q^{96} + 28 q^{97} - 56 q^{98} + O(q^{100}) \)

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

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