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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

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

Display 100 coefficients 10 coefficients

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

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