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Properties

Label 2842.2.cz
Level $2842$
Weight $2$
Character orbit 2842.cz
Rep. character $\chi_{2842}(151,\cdot)$
Character field $\Q(\zeta_{42})$
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.cz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
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 5088 1680 3408
Cusp forms 4992 1680 3312
Eisenstein series 96 0 96

Trace form

\( 1680 q - 140 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 164 q^{9} + O(q^{10}) \) \( 1680 q - 140 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 164 q^{9} + 14 q^{10} - 8 q^{13} + 14 q^{15} + 140 q^{16} - 56 q^{17} + 8 q^{20} + 70 q^{21} + 16 q^{22} - 30 q^{23} - 22 q^{24} + 144 q^{25} + 4 q^{28} + 22 q^{29} + 4 q^{30} - 28 q^{31} + 2 q^{33} - 56 q^{34} - 64 q^{35} - 286 q^{36} + 84 q^{37} - 54 q^{38} + 98 q^{41} + 38 q^{42} + 28 q^{43} - 108 q^{45} - 56 q^{47} - 14 q^{49} + 12 q^{51} - 4 q^{52} + 46 q^{53} + 104 q^{54} + 16 q^{57} - 4 q^{58} + 40 q^{59} - 28 q^{60} - 14 q^{61} - 16 q^{62} - 28 q^{63} + 280 q^{64} + 30 q^{65} + 8 q^{67} + 70 q^{68} + 140 q^{69} - 58 q^{71} + 84 q^{73} - 12 q^{74} + 224 q^{75} + 70 q^{77} - 24 q^{78} + 4 q^{80} + 204 q^{81} - 24 q^{82} - 4 q^{83} + 42 q^{84} - 12 q^{86} - 46 q^{87} + 22 q^{88} - 126 q^{89} + 56 q^{90} + 36 q^{91} + 24 q^{92} + 30 q^{93} - 16 q^{94} - 224 q^{95} - 20 q^{96} + 14 q^{97} + O(q^{100}) \)

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

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