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Properties

Label 1859.4.bf
Level $1859$
Weight $4$
Character orbit 1859.bf
Rep. character $\chi_{1859}(14,\cdot)$
Character field $\Q(\zeta_{65})$
Dimension $26112$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.bf (of order \(65\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{65})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 26304 26304 0
Cusp forms 26112 26112 0
Eisenstein series 192 192 0

Trace form

\( 26112 q - 33 q^{2} - 33 q^{3} + 2135 q^{4} - 33 q^{5} - 65 q^{6} - 33 q^{7} - 65 q^{8} + 4731 q^{9} + O(q^{10}) \) \( 26112 q - 33 q^{2} - 33 q^{3} + 2135 q^{4} - 33 q^{5} - 65 q^{6} - 33 q^{7} - 65 q^{8} + 4731 q^{9} - 280 q^{10} - 88 q^{11} - 228 q^{12} + 63 q^{14} + 27 q^{15} + 8599 q^{16} + 71 q^{17} + 51 q^{18} - 256 q^{19} - 851 q^{20} - 340 q^{21} - 990 q^{22} - 600 q^{23} - 153 q^{24} + 13655 q^{25} + 101 q^{26} + 171 q^{27} - 249 q^{28} - 461 q^{29} + 5145 q^{30} - 2629 q^{31} - 96 q^{32} - 1566 q^{33} - 1438 q^{34} - 865 q^{35} + 20713 q^{36} + 303 q^{37} - 423 q^{38} - 716 q^{39} - 521 q^{40} - 1493 q^{41} - 501 q^{42} + 1032 q^{43} + 58 q^{44} - 1232 q^{45} + 791 q^{46} + 1291 q^{47} + 595 q^{48} + 28609 q^{49} - 735 q^{50} + 355 q^{51} - 6820 q^{52} + 191 q^{53} + 6380 q^{54} + 342 q^{55} - 1652 q^{56} + 4785 q^{57} + 527 q^{58} - 5605 q^{59} + 7897 q^{60} + 699 q^{61} + 6669 q^{62} + 2305 q^{63} + 32543 q^{64} + 186 q^{65} + 5685 q^{66} + 22480 q^{67} - 3723 q^{68} + 2868 q^{69} - 10874 q^{70} - 10161 q^{71} - 18655 q^{72} - 1281 q^{73} + 2809 q^{74} + 13163 q^{75} - 22164 q^{76} + 394 q^{77} - 20344 q^{78} + 5187 q^{79} + 11892 q^{80} + 52091 q^{81} + 19033 q^{82} - 13729 q^{83} + 5341 q^{84} - 821 q^{85} - 4001 q^{86} + 2788 q^{87} - 5970 q^{88} - 28760 q^{89} + 3157 q^{90} + 450 q^{91} + 2981 q^{92} + 9683 q^{93} + 36755 q^{94} + 8209 q^{95} - 3829 q^{96} - 10335 q^{97} + 1476 q^{98} - 696 q^{99} + O(q^{100}) \)

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.