↑

Properties

Label 2842.2.ec
Level $2842$
Weight $2$
Character orbit 2842.ec
Rep. character $\chi_{2842}(3,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3360$
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.ec (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 10176 3360 6816
Cusp forms 9984 3360 6624
Eisenstein series 192 0 192

Trace form

\( 3360 q + O(q^{10}) \) \( 3360 q + 12 q^{10} + 4 q^{14} + 32 q^{15} - 280 q^{16} - 24 q^{17} - 20 q^{21} + 24 q^{24} + 280 q^{25} + 4 q^{29} + 36 q^{31} - 84 q^{35} - 548 q^{36} - 4 q^{37} - 56 q^{38} + 96 q^{39} - 12 q^{40} - 84 q^{41} - 40 q^{43} + 12 q^{46} - 4 q^{47} + 8 q^{49} - 16 q^{50} - 8 q^{53} + 16 q^{54} + 112 q^{55} - 20 q^{56} - 16 q^{58} - 168 q^{59} - 16 q^{60} + 24 q^{61} + 24 q^{65} + 176 q^{66} - 52 q^{68} + 52 q^{70} - 84 q^{71} - 36 q^{73} + 24 q^{74} - 60 q^{75} - 8 q^{77} + 64 q^{78} - 16 q^{79} + 1728 q^{81} + 112 q^{83} + 28 q^{84} + 88 q^{85} - 440 q^{87} - 60 q^{89} + 24 q^{94} + 104 q^{95} + 336 q^{97} - 88 q^{98} - 20 q^{99} + O(q^{100}) \)

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

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