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Properties

Label 2842.2.cg
Level $2842$
Weight $2$
Character orbit 2842.cg
Rep. character $\chi_{2842}(503,\cdot)$
Character field $\Q(\zeta_{28})$
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.cg (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{28})\)
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

\( 1680 q + O(q^{10}) \) \( 1680 q - 28 q^{10} + 8 q^{14} - 4 q^{15} - 1680 q^{16} - 84 q^{21} - 28 q^{24} - 280 q^{25} + 28 q^{28} + 24 q^{29} - 28 q^{31} - 84 q^{35} - 292 q^{36} - 8 q^{37} - 28 q^{38} - 60 q^{39} - 16 q^{43} - 60 q^{46} - 44 q^{49} + 16 q^{50} - 16 q^{53} - 28 q^{54} - 112 q^{55} - 8 q^{56} + 140 q^{57} - 32 q^{58} - 56 q^{59} - 4 q^{60} + 48 q^{65} - 28 q^{69} - 4 q^{70} + 84 q^{71} - 36 q^{74} + 8 q^{77} - 64 q^{78} + 80 q^{79} + 432 q^{81} + 56 q^{83} - 88 q^{85} + 28 q^{86} - 224 q^{87} - 112 q^{89} - 112 q^{90} + 84 q^{91} - 84 q^{92} - 168 q^{93} + 40 q^{95} - 28 q^{97} - 64 q^{99} + O(q^{100}) \)

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

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