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Properties

Label 1859.4.bo
Level $1859$
Weight $4$
Character orbit 1859.bo
Rep. character $\chi_{1859}(3,\cdot)$
Character field $\Q(\zeta_{195})$
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.bo (of order \(195\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{195})\)
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

\( 52224 q - 75 q^{2} - 75 q^{3} - 2243 q^{4} - 66 q^{5} - 43 q^{6} - 75 q^{7} - 34 q^{8} - 4983 q^{9} + O(q^{10}) \) \( 52224 q - 75 q^{2} - 75 q^{3} - 2243 q^{4} - 66 q^{5} - 43 q^{6} - 75 q^{7} - 34 q^{8} - 4983 q^{9} - 56 q^{10} - 134 q^{11} - 36 q^{12} + 36 q^{13} - 162 q^{14} - 45 q^{15} - 8671 q^{16} - 227 q^{17} - 150 q^{18} - 56 q^{19} + 299 q^{20} + 316 q^{21} - 471 q^{22} - 300 q^{23} + 1059 q^{24} + 26446 q^{25} - 710 q^{26} - 270 q^{27} + 201 q^{28} - 811 q^{29} + 11085 q^{30} + 2470 q^{31} - 156 q^{32} + 1140 q^{33} + 6550 q^{34} - 1331 q^{35} - 18154 q^{36} - 411 q^{37} + 324 q^{38} + 1028 q^{39} + 362 q^{40} + 1673 q^{41} + 987 q^{42} + 2424 q^{43} + 44 q^{44} + 74 q^{45} - 251 q^{46} + 3110 q^{47} + 449 q^{48} - 29419 q^{49} - 426 q^{50} - 838 q^{51} + 8008 q^{52} - 1682 q^{53} - 8534 q^{54} + 2415 q^{55} - 6358 q^{56} - 4884 q^{57} + 253 q^{58} - 7925 q^{59} - 5746 q^{60} - 807 q^{61} - 6507 q^{62} - 8158 q^{63} + 61558 q^{64} - 2532 q^{65} + 21375 q^{66} - 21232 q^{67} - 3984 q^{68} + 4512 q^{69} + 6998 q^{70} - 11841 q^{71} + 14653 q^{72} + 894 q^{73} - 5101 q^{74} - 8987 q^{75} - 84270 q^{76} - 2182 q^{77} + 16480 q^{78} - 546 q^{79} - 8670 q^{80} - 38165 q^{81} - 23839 q^{82} - 19226 q^{83} + 4982 q^{84} - 469 q^{85} - 190 q^{86} - 3856 q^{87} - 12315 q^{88} + 14420 q^{89} + 644 q^{90} + 4524 q^{91} - 3080 q^{92} - 2003 q^{93} - 54839 q^{94} - q^{95} + 21586 q^{96} + 9543 q^{97} - 5310 q^{98} + 5604 q^{99} + O(q^{100}) \)

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.