Properties

Label 1840.2.ch
Level $1840$
Weight $2$
Character orbit 1840.ch
Rep. character $\chi_{1840}(3,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $5680$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.ch (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1840 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

Total New Old
Modular forms 5840 5840 0
Cusp forms 5680 5680 0
Eisenstein series 160 160 0

Trace form

\( 5680q - 18q^{2} - 36q^{3} - 8q^{4} - 18q^{5} - 36q^{6} - 36q^{7} - 18q^{8} - 552q^{9} + O(q^{10}) \) \( 5680q - 18q^{2} - 36q^{3} - 8q^{4} - 18q^{5} - 36q^{6} - 36q^{7} - 18q^{8} - 552q^{9} - 26q^{10} - 36q^{11} - 6q^{12} + 24q^{15} - 28q^{16} - 36q^{17} + 2q^{18} + 16q^{19} - 18q^{20} - 36q^{21} - 52q^{22} - 40q^{23} + 24q^{24} - 36q^{26} - 12q^{27} - 66q^{28} - 38q^{30} - 38q^{32} - 36q^{33} - 32q^{34} - 38q^{35} - 36q^{36} - 26q^{38} - 58q^{40} + 190q^{42} - 216q^{44} - 8q^{45} - 56q^{46} - 90q^{48} - 38q^{50} - 52q^{51} + 182q^{52} - 36q^{53} + 40q^{54} - 36q^{55} - 84q^{56} + 24q^{57} - 42q^{58} - 62q^{60} - 68q^{61} - 10q^{62} + 24q^{63} - 32q^{64} - 36q^{65} - 36q^{66} - 4q^{68} + 28q^{69} - 44q^{70} - 72q^{71} - 40q^{72} + 16q^{74} - 6q^{75} - 36q^{76} + 20q^{77} - 90q^{78} + 22q^{80} - 576q^{81} - 26q^{82} - 116q^{83} + 24q^{84} - 38q^{85} - 4q^{86} - 36q^{87} - 50q^{88} - 10q^{90} - 80q^{91} - 18q^{92} + 8q^{94} - 80q^{95} - 36q^{96} - 36q^{97} - 26q^{98} + 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.