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Properties

Label 2842.2.dd
Level $2842$
Weight $2$
Character orbit 2842.dd
Rep. character $\chi_{2842}(67,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1200$
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.dd (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 203 \)
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 5232 1200 4032
Cusp forms 4848 1200 3648
Eisenstein series 384 0 384

Trace form

\( 1200 q - 100 q^{4} - 4 q^{5} - 12 q^{6} - 120 q^{9} + O(q^{10}) \) \( 1200 q - 100 q^{4} - 4 q^{5} - 12 q^{6} - 120 q^{9} + 8 q^{13} - 28 q^{15} + 100 q^{16} - 8 q^{20} + 12 q^{22} + 46 q^{23} - 6 q^{24} + 150 q^{25} + 168 q^{27} + 80 q^{29} - 4 q^{30} - 28 q^{31} - 72 q^{33} - 212 q^{36} + 42 q^{37} - 30 q^{38} + 56 q^{39} - 56 q^{44} - 4 q^{45} + 28 q^{47} - 56 q^{50} + 44 q^{51} + 4 q^{52} - 64 q^{53} + 8 q^{54} + 112 q^{55} + 176 q^{57} + 24 q^{58} - 68 q^{59} + 14 q^{60} + 16 q^{62} + 200 q^{64} - 104 q^{65} + 60 q^{67} + 14 q^{68} + 56 q^{69} - 48 q^{71} - 54 q^{74} + 48 q^{78} - 4 q^{80} - 116 q^{81} - 32 q^{82} - 80 q^{83} + 168 q^{85} + 12 q^{86} - 10 q^{87} - 8 q^{88} + 92 q^{92} + 92 q^{93} - 40 q^{94} - 336 q^{95} - 8 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2842, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(203, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(406, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1421, [\chi])\)\(^{\oplus 2}\)