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Properties

Label 1859.4.bp
Level $1859$
Weight $4$
Character orbit 1859.bp
Rep. character $\chi_{1859}(8,\cdot)$
Character field $\Q(\zeta_{260})$
Dimension $52224$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.bp (of order \(260\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{260})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 52608 52608 0
Cusp forms 52224 52224 0
Eisenstein series 384 384 0

Trace form

\( 52224 q - 120 q^{2} - 66 q^{3} - 78 q^{4} - 72 q^{5} - 120 q^{6} - 120 q^{7} - 120 q^{8} + 9654 q^{9} + O(q^{10}) \) \( 52224 q - 120 q^{2} - 66 q^{3} - 78 q^{4} - 72 q^{5} - 120 q^{6} - 120 q^{7} - 120 q^{8} + 9654 q^{9} + 20 q^{11} - 208 q^{12} - 160 q^{13} + 142 q^{14} - 348 q^{15} - 17282 q^{16} - 130 q^{17} - 120 q^{18} - 120 q^{19} + 762 q^{20} - 452 q^{22} - 1100 q^{24} - 78 q^{25} - 576 q^{26} - 906 q^{27} - 120 q^{28} - 110 q^{29} - 130 q^{30} + 140 q^{31} - 834 q^{33} - 2300 q^{34} + 2490 q^{35} - 78 q^{36} - 408 q^{37} - 78 q^{38} - 1960 q^{39} + 1170 q^{40} + 2100 q^{41} + 1590 q^{42} - 946 q^{44} - 1336 q^{45} + 120 q^{46} + 832 q^{47} + 1446 q^{48} - 78 q^{49} + 1130 q^{50} - 130 q^{51} - 17520 q^{52} - 6306 q^{53} - 6640 q^{55} - 208 q^{56} - 120 q^{57} - 1320 q^{58} + 868 q^{59} - 10730 q^{60} - 110 q^{61} - 130 q^{62} - 5110 q^{63} - 78 q^{64} + 21098 q^{66} + 49656 q^{67} - 110 q^{68} + 2028 q^{69} - 9370 q^{70} + 6276 q^{71} + 4440 q^{72} - 2040 q^{73} - 110 q^{74} + 24362 q^{75} - 104 q^{77} - 34060 q^{78} - 9470 q^{79} + 13108 q^{80} + 78182 q^{81} + 44382 q^{82} - 1540 q^{83} - 9470 q^{84} + 40 q^{85} - 5668 q^{86} + 1560 q^{88} - 15464 q^{89} - 130 q^{90} + 3064 q^{91} + 830 q^{92} + 17216 q^{93} + 15490 q^{94} - 130 q^{95} - 21730 q^{96} - 19380 q^{97} - 3944 q^{99} + O(q^{100}) \)

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.