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Properties

Label 1859.4.bv
Level $1859$
Weight $4$
Character orbit 1859.bv
Rep. character $\chi_{1859}(2,\cdot)$
Character field $\Q(\zeta_{780})$
Dimension $104448$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.bv (of order \(780\) and degree \(192\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{780})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1859, [\chi])\).

Total New Old
Modular forms 105216 105216 0
Cusp forms 104448 104448 0
Eisenstein series 768 768 0

Trace form

\( 104448 q - 240 q^{2} - 150 q^{3} - 138 q^{4} - 144 q^{5} - 240 q^{6} - 240 q^{7} - 240 q^{8} - 9870 q^{9} + O(q^{10}) \) \( 104448 q - 240 q^{2} - 150 q^{3} - 138 q^{4} - 144 q^{5} - 240 q^{6} - 240 q^{7} - 240 q^{8} - 9870 q^{9} - 68 q^{11} - 416 q^{12} - 200 q^{13} - 340 q^{14} - 12 q^{15} + 17066 q^{16} - 230 q^{17} - 240 q^{18} - 240 q^{19} - 1098 q^{20} - 226 q^{22} + 336 q^{23} + 500 q^{24} - 156 q^{25} + 360 q^{26} + 708 q^{27} - 240 q^{28} - 250 q^{29} - 230 q^{30} - 416 q^{31} + 1146 q^{33} - 1924 q^{34} + 1050 q^{35} - 3696 q^{36} + 192 q^{37} - 156 q^{38} + 1600 q^{39} - 1500 q^{40} - 2460 q^{41} + 678 q^{42} + 124 q^{44} + 520 q^{45} - 2640 q^{46} + 2408 q^{47} + 930 q^{48} - 138 q^{49} - 1490 q^{50} - 260 q^{51} + 17160 q^{52} + 6108 q^{53} + 8692 q^{55} - 1712 q^{56} - 240 q^{57} + 2400 q^{58} + 512 q^{59} + 8264 q^{60} - 250 q^{61} - 230 q^{62} + 4750 q^{63} - 156 q^{64} - 21362 q^{66} - 47448 q^{67} - 250 q^{68} - 2244 q^{69} + 9814 q^{70} - 1452 q^{71} - 11280 q^{72} + 1680 q^{73} - 250 q^{74} - 15734 q^{75} - 208 q^{77} + 24988 q^{78} + 9140 q^{79} - 12268 q^{80} - 89330 q^{81} - 35202 q^{82} + 4240 q^{83} - 1180 q^{84} - 400 q^{85} + 11104 q^{86} + 8310 q^{88} + 22592 q^{89} - 260 q^{90} - 10144 q^{91} - 1028 q^{92} - 40076 q^{93} + 7550 q^{94} + 9070 q^{95} + 6010 q^{96} + 16968 q^{97} - 7084 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

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