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Properties

Label 1859.2.bp
Level $1859$
Weight $2$
Character orbit 1859.bp
Rep. character $\chi_{1859}(8,\cdot)$
Character field $\Q(\zeta_{260})$
Dimension $17280$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.bp (of order \(260\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{260})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1859, [\chi])\).

Total New Old
Modular forms 17664 17664 0
Cusp forms 17280 17280 0
Eisenstein series 384 384 0

Trace form

\( 17280 q - 120 q^{2} - 66 q^{3} - 78 q^{4} - 72 q^{5} - 120 q^{6} - 120 q^{7} - 120 q^{8} + 286 q^{9} + O(q^{10}) \) \( 17280 q - 120 q^{2} - 66 q^{3} - 78 q^{4} - 72 q^{5} - 120 q^{6} - 120 q^{7} - 120 q^{8} + 286 q^{9} - 112 q^{11} - 208 q^{12} - 110 q^{13} - 82 q^{14} - 88 q^{15} - 414 q^{16} - 130 q^{17} - 120 q^{18} - 120 q^{19} - 82 q^{20} - 172 q^{22} - 80 q^{24} - 78 q^{25} - 44 q^{26} - 66 q^{27} - 120 q^{28} - 110 q^{29} - 130 q^{30} - 96 q^{31} - 56 q^{33} - 252 q^{34} - 210 q^{35} - 78 q^{36} - 60 q^{37} - 78 q^{38} - 40 q^{39} - 30 q^{40} - 180 q^{41} - 42 q^{42} - 142 q^{44} - 268 q^{45} + 80 q^{46} - 106 q^{47} - 202 q^{48} - 78 q^{49} - 70 q^{50} - 130 q^{51} - 720 q^{52} - 78 q^{53} + 100 q^{55} - 208 q^{56} - 120 q^{57} - 92 q^{58} - 82 q^{59} + 514 q^{60} - 110 q^{61} - 130 q^{62} - 70 q^{63} - 78 q^{64} - 150 q^{66} - 940 q^{67} - 110 q^{68} + 156 q^{69} + 130 q^{70} - 104 q^{71} - 300 q^{72} - 90 q^{73} - 110 q^{74} + 182 q^{75} - 104 q^{77} + 116 q^{78} - 190 q^{79} + 4 q^{80} + 246 q^{81} - 858 q^{82} - 20 q^{83} - 350 q^{84} - 160 q^{85} - 524 q^{86} + 4 q^{89} - 130 q^{90} - 116 q^{91} + 166 q^{92} - 528 q^{93} - 310 q^{94} - 130 q^{95} + 30 q^{96} - 506 q^{97} - 174 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

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