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Properties

Label 1840.3.ce
Level $1840$
Weight $3$
Character orbit 1840.ce
Rep. character $\chi_{1840}(77,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $11440$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1840.ce (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1840 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1840, [\chi])\).

Total New Old
Modular forms 11600 11600 0
Cusp forms 11440 11440 0
Eisenstein series 160 160 0

Trace form

\( 11440 q - 18 q^{2} - 36 q^{3} + 8 q^{4} - 18 q^{5} - 36 q^{6} - 18 q^{8} - 3384 q^{9} + O(q^{10}) \) \( 11440 q - 18 q^{2} - 36 q^{3} + 8 q^{4} - 18 q^{5} - 36 q^{6} - 18 q^{8} - 3384 q^{9} - 2 q^{10} - 36 q^{11} + 18 q^{12} - 36 q^{13} - 36 q^{15} - 92 q^{16} - 36 q^{17} + 34 q^{18} + 64 q^{19} - 18 q^{20} - 36 q^{21} + 36 q^{22} + 72 q^{24} - 36 q^{26} + 36 q^{27} + 78 q^{28} + 114 q^{30} - 72 q^{31} + 122 q^{32} - 36 q^{33} - 32 q^{34} + 82 q^{35} + 188 q^{36} - 36 q^{37} - 34 q^{38} + 144 q^{39} - 338 q^{40} + 430 q^{42} + 216 q^{44} + 96 q^{45} - 152 q^{46} - 80 q^{47} - 322 q^{48} - 238 q^{50} + 156 q^{51} + 1198 q^{52} + 104 q^{54} + 300 q^{56} + 72 q^{57} - 386 q^{58} - 310 q^{60} + 28 q^{61} - 10 q^{62} + 356 q^{63} - 352 q^{64} - 36 q^{65} - 36 q^{66} - 572 q^{68} - 60 q^{69} - 796 q^{70} + 76 q^{72} + 64 q^{74} + 18 q^{75} - 548 q^{76} + 750 q^{78} + 22 q^{80} - 9792 q^{81} + 606 q^{82} - 356 q^{83} + 72 q^{84} + 82 q^{85} + 188 q^{86} + 72 q^{87} - 274 q^{88} + 458 q^{90} - 80 q^{91} + 330 q^{92} - 8 q^{93} - 152 q^{94} - 36 q^{95} - 36 q^{96} - 36 q^{97} + 190 q^{98} + 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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