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Properties

Label 2842.2.cf
Level $2842$
Weight $2$
Character orbit 2842.cf
Rep. character $\chi_{2842}(69,\cdot)$
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.cf (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

\( 1680 q + O(q^{10}) \) \( 1680 q + 8 q^{14} - 32 q^{15} + 280 q^{16} - 280 q^{25} + 84 q^{27} - 28 q^{28} + 24 q^{29} + 28 q^{31} - 292 q^{36} + 76 q^{37} - 28 q^{38} + 24 q^{39} - 112 q^{41} + 40 q^{43} + 24 q^{46} - 16 q^{49} + 16 q^{50} - 16 q^{53} + 112 q^{54} - 112 q^{55} - 8 q^{56} - 140 q^{57} - 32 q^{58} - 56 q^{59} - 32 q^{60} + 84 q^{61} + 84 q^{63} - 36 q^{65} - 112 q^{66} - 140 q^{69} - 116 q^{70} - 28 q^{71} - 28 q^{73} + 48 q^{74} + 36 q^{77} + 48 q^{78} + 80 q^{79} + 236 q^{81} + 28 q^{84} - 32 q^{85} - 28 q^{86} + 28 q^{89} - 112 q^{91} + 40 q^{95} + 28 q^{97} - 64 q^{99} + O(q^{100}) \)

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

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