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Properties

Label 1849.2.e
Level $1849$
Weight $2$
Character orbit 1849.e
Rep. character $\chi_{1849}(78,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $786$
Sturm bound $315$

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Defining parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1849.e (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(315\)

Dimensions

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

Total New Old
Modular forms 1074 1026 48
Cusp forms 810 786 24
Eisenstein series 264 240 24

Trace form

\( 786 q + 2 q^{2} + q^{3} - 110 q^{4} + q^{5} + 2 q^{6} + 16 q^{7} + 6 q^{8} - 84 q^{9} + O(q^{10}) \) \( 786 q + 2 q^{2} + q^{3} - 110 q^{4} + q^{5} + 2 q^{6} + 16 q^{7} + 6 q^{8} - 84 q^{9} - 7 q^{10} - 5 q^{11} - 11 q^{12} + 3 q^{13} + 15 q^{14} + 9 q^{15} - 78 q^{16} - 5 q^{17} - 13 q^{18} + 2 q^{19} - 15 q^{20} - 8 q^{21} - 6 q^{22} - 3 q^{23} + 4 q^{24} - 46 q^{25} - 3 q^{26} - 29 q^{27} - 21 q^{28} - 15 q^{29} + 16 q^{30} + 23 q^{31} + 36 q^{32} - 20 q^{33} - 12 q^{34} - 4 q^{35} + 184 q^{36} + 18 q^{37} + 27 q^{38} - 5 q^{39} - 19 q^{40} - 26 q^{41} + 38 q^{42} - 166 q^{44} + 26 q^{45} - 16 q^{46} - 22 q^{47} - 11 q^{48} + 46 q^{49} - 12 q^{50} + 24 q^{51} - 7 q^{52} + 11 q^{53} - 56 q^{54} - 19 q^{55} - 23 q^{56} + 9 q^{57} + 25 q^{58} - 38 q^{59} - 47 q^{60} - 31 q^{61} - 45 q^{62} - 9 q^{63} - 14 q^{64} - 19 q^{65} - 37 q^{66} + 21 q^{67} - 10 q^{68} - q^{69} + 26 q^{70} - 54 q^{71} + 29 q^{72} - 12 q^{73} - 12 q^{74} - 11 q^{75} - 32 q^{76} + 21 q^{77} - 24 q^{78} + 38 q^{79} + 38 q^{80} + 117 q^{81} + 3 q^{82} + 18 q^{83} + 28 q^{85} - 158 q^{87} + 28 q^{88} - 22 q^{89} + 76 q^{90} + 4 q^{91} + 36 q^{92} + 28 q^{93} + 23 q^{94} - 3 q^{95} - 44 q^{96} - 14 q^{97} - 26 q^{98} - 9 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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