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Properties

Label 2842.2.ch
Level $2842$
Weight $2$
Character orbit 2842.ch
Rep. character $\chi_{2842}(55,\cdot)$
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.ch (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

\( 1680 q + O(q^{10}) \) \( 1680 q + 8 q^{14} + 52 q^{15} + 280 q^{16} - 56 q^{17} + 28 q^{21} + 28 q^{24} - 280 q^{25} + 24 q^{29} - 292 q^{36} + 20 q^{37} - 56 q^{38} + 24 q^{39} - 56 q^{41} - 16 q^{43} + 24 q^{46} + 40 q^{49} + 16 q^{50} + 40 q^{53} - 140 q^{55} - 8 q^{56} - 32 q^{58} - 84 q^{59} + 52 q^{60} + 224 q^{63} - 120 q^{65} - 28 q^{68} + 168 q^{69} - 4 q^{70} + 84 q^{71} + 84 q^{73} + 48 q^{74} + 224 q^{75} - 76 q^{77} + 48 q^{78} - 32 q^{79} + 432 q^{81} - 32 q^{85} - 84 q^{86} + 112 q^{91} + 168 q^{93} - 28 q^{94} + 40 q^{95} - 168 q^{97} + 20 q^{99} + O(q^{100}) \)

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

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