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Properties

Label 2842.2.cy
Level $2842$
Weight $2$
Character orbit 2842.cy
Rep. character $\chi_{2842}(93,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1680$
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.cy (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 5088 1680 3408
Cusp forms 4992 1680 3312
Eisenstein series 96 0 96

Trace form

\( 1680 q + 840 q^{4} + 4 q^{5} - 2 q^{6} + 10 q^{7} - 164 q^{9} + O(q^{10}) \) \( 1680 q + 840 q^{4} + 4 q^{5} - 2 q^{6} + 10 q^{7} - 164 q^{9} + 28 q^{10} - 8 q^{13} - 840 q^{16} + 8 q^{20} - 42 q^{21} + 16 q^{22} + 54 q^{23} + 20 q^{24} + 158 q^{25} - 10 q^{28} + 8 q^{29} + 4 q^{30} + 28 q^{31} - 40 q^{33} + 34 q^{35} - 286 q^{36} + 16 q^{38} + 84 q^{39} + 14 q^{40} + 56 q^{41} + 24 q^{42} + 46 q^{45} - 42 q^{46} - 56 q^{47} + 14 q^{49} + 54 q^{51} - 4 q^{52} + 32 q^{53} - 64 q^{54} - 56 q^{55} - 54 q^{57} - 4 q^{58} - 16 q^{59} - 42 q^{60} - 16 q^{62} + 70 q^{63} - 1680 q^{64} - 12 q^{65} + 36 q^{67} - 112 q^{69} - 112 q^{70} + 40 q^{71} - 54 q^{74} + 14 q^{77} + 32 q^{78} + 4 q^{80} + 78 q^{81} + 4 q^{82} + 80 q^{83} + 42 q^{84} + 30 q^{86} - 18 q^{87} + 8 q^{88} - 56 q^{89} - 56 q^{90} - 34 q^{91} - 18 q^{92} + 30 q^{93} - 44 q^{94} + 22 q^{96} + 14 q^{97} + O(q^{100}) \)

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

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