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Properties

Label 1859.4.bn
Level $1859$
Weight $4$
Character orbit 1859.bn
Rep. character $\chi_{1859}(32,\cdot)$
Character field $\Q(\zeta_{156})$
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.bn (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{156})\)
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

\( 26112 q - 100 q^{3} - 92 q^{4} - 96 q^{5} + 9620 q^{9} + O(q^{10}) \) \( 26112 q - 100 q^{3} - 92 q^{4} - 96 q^{5} + 9620 q^{9} + 28 q^{11} - 104 q^{12} + 120 q^{14} - 28 q^{15} - 17316 q^{16} - 172 q^{20} + 106 q^{22} + 84 q^{23} - 104 q^{25} - 600 q^{26} - 928 q^{27} + 176 q^{31} + 214 q^{33} - 2316 q^{34} + 2656 q^{36} - 432 q^{37} - 104 q^{38} - 928 q^{42} - 364 q^{44} - 1000 q^{45} - 108 q^{47} - 1820 q^{48} - 92 q^{49} + 4072 q^{53} - 8942 q^{55} + 1252 q^{56} - 1200 q^{58} + 1288 q^{59} + 9876 q^{60} - 104 q^{64} - 1998 q^{66} - 13512 q^{67} - 1496 q^{69} - 9404 q^{70} + 4972 q^{71} + 15504 q^{75} - 52 q^{77} - 25108 q^{78} - 4692 q^{80} + 84920 q^{81} - 22028 q^{82} - 1344 q^{86} - 8540 q^{88} - 28172 q^{89} + 904 q^{91} - 6232 q^{92} - 20524 q^{93} + 11832 q^{97} + 6944 q^{99} + O(q^{100}) \)

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.