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Properties

Label 1859.4.r
Level $1859$
Weight $4$
Character orbit 1859.r
Rep. character $\chi_{1859}(146,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $3616$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 4480 3776 704
Cusp forms 4256 3616 640
Eisenstein series 224 160 64

Trace form

\( 3616 q + 3 q^{2} + 3 q^{3} + 1771 q^{4} + 12 q^{5} + 35 q^{6} + 3 q^{7} + 44 q^{8} + 3843 q^{9} + O(q^{10}) \) \( 3616 q + 3 q^{2} + 3 q^{3} + 1771 q^{4} + 12 q^{5} + 35 q^{6} + 3 q^{7} + 44 q^{8} + 3843 q^{9} + 8 q^{10} - 30 q^{11} + 268 q^{12} + 4 q^{14} + 33 q^{15} + 6551 q^{16} - 137 q^{17} - 72 q^{18} - 17 q^{19} + 377 q^{20} + 524 q^{21} - 147 q^{22} - 196 q^{23} + 1137 q^{24} - 20876 q^{25} - 264 q^{27} + 279 q^{28} - 1153 q^{29} - 2421 q^{30} - 260 q^{31} + 52 q^{32} + 1244 q^{33} + 3508 q^{34} - 1253 q^{35} + 14920 q^{36} - 333 q^{37} + 778 q^{38} + 80 q^{40} + 1751 q^{41} + 725 q^{42} + 1768 q^{43} + 252 q^{44} + 282 q^{45} - 485 q^{46} - 2116 q^{47} + 475 q^{48} + 18969 q^{49} - 348 q^{50} - 2776 q^{51} + 676 q^{53} - 8326 q^{54} + 1331 q^{55} - 9302 q^{56} + 888 q^{57} + 331 q^{58} + 1097 q^{59} + 1820 q^{60} - 1041 q^{61} - 367 q^{62} - 540 q^{63} - 51644 q^{64} + 1310 q^{66} + 5184 q^{67} - 5298 q^{68} + 6273 q^{69} - 4078 q^{70} - 843 q^{71} - 1155 q^{72} + 972 q^{73} - 6239 q^{74} + 3551 q^{75} + 3090 q^{76} + 874 q^{77} - 1884 q^{79} - 8631 q^{80} + 36957 q^{81} - 6691 q^{82} + 5292 q^{83} + 5060 q^{84} - 391 q^{85} - 3388 q^{86} + 6344 q^{87} + 12317 q^{88} - 6276 q^{89} - 9470 q^{90} - 10890 q^{92} + 2599 q^{93} - 14669 q^{94} - 2529 q^{95} + 30114 q^{96} - 1377 q^{97} - 5102 q^{98} + 5812 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1859, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1859, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)