Properties

Label 1849.2.c
Level $1849$
Weight $2$
Character orbit 1849.c
Rep. character $\chi_{1849}(423,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $260$
Sturm bound $315$

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Defining parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1849.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(315\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1849, [\chi])\).

Total New Old
Modular forms 360 340 20
Cusp forms 272 260 12
Eisenstein series 88 80 8

Trace form

\( 260 q + 4 q^{2} - 2 q^{3} + 220 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} + 18 q^{8} - 92 q^{9} + O(q^{10}) \) \( 260 q + 4 q^{2} - 2 q^{3} + 220 q^{4} - 3 q^{5} + 3 q^{6} - q^{7} + 18 q^{8} - 92 q^{9} + 7 q^{10} + 12 q^{11} + 2 q^{12} - q^{13} + 4 q^{14} - 3 q^{15} + 116 q^{16} + 3 q^{17} + 4 q^{18} + 3 q^{19} - 17 q^{20} - 28 q^{21} - 10 q^{22} + 3 q^{23} - 4 q^{24} - 51 q^{25} - 15 q^{26} + 10 q^{27} + 6 q^{28} + 9 q^{29} - 3 q^{30} + 4 q^{31} + 20 q^{32} + 10 q^{33} + 14 q^{34} + 18 q^{35} - 47 q^{36} - 12 q^{37} - 7 q^{38} + 20 q^{39} + 29 q^{40} + 2 q^{41} + 2 q^{42} - 76 q^{44} - 32 q^{45} - 26 q^{46} + 6 q^{47} - 13 q^{48} - q^{49} - 17 q^{50} + 22 q^{51} + 16 q^{52} - 11 q^{53} + 48 q^{54} - 31 q^{56} + 3 q^{57} - 6 q^{58} - 14 q^{59} - q^{60} - 14 q^{61} + 5 q^{62} - 23 q^{63} - 50 q^{64} + 10 q^{65} - 19 q^{66} - 5 q^{67} - 43 q^{68} - 21 q^{69} - 2 q^{70} + 2 q^{71} + 33 q^{72} + 8 q^{73} - 26 q^{74} - 6 q^{75} + 17 q^{76} + 15 q^{77} - 14 q^{79} - 27 q^{80} + 38 q^{81} + 30 q^{82} + 11 q^{83} + 76 q^{84} - 42 q^{85} - 52 q^{87} - 10 q^{88} + 2 q^{89} - 100 q^{90} - 20 q^{91} + 27 q^{92} + 5 q^{93} + 58 q^{94} - 23 q^{95} + 6 q^{96} + 42 q^{97} + 16 q^{98} - 15 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1849, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1849, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1849, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)