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Properties

Label 1859.2.bn
Level $1859$
Weight $2$
Character orbit 1859.bn
Rep. character $\chi_{1859}(32,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $8640$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.bn (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1859, [\chi])\).

Total New Old
Modular forms 8832 8832 0
Cusp forms 8640 8640 0
Eisenstein series 192 192 0

Trace form

\( 8640 q - 100 q^{3} - 92 q^{4} - 96 q^{5} + 252 q^{9} + O(q^{10}) \) \( 8640 q - 100 q^{3} - 92 q^{4} - 96 q^{5} + 252 q^{9} - 60 q^{11} - 104 q^{12} - 104 q^{14} - 116 q^{15} - 448 q^{16} - 52 q^{20} - 34 q^{22} - 156 q^{23} - 104 q^{25} - 68 q^{26} - 88 q^{27} - 108 q^{31} - 100 q^{33} - 92 q^{34} - 224 q^{36} - 84 q^{37} - 104 q^{38} - 112 q^{42} - 112 q^{44} - 112 q^{45} - 144 q^{47} - 108 q^{48} - 92 q^{49} - 80 q^{53} + 168 q^{55} + 28 q^{56} - 132 q^{58} - 64 q^{59} - 540 q^{60} - 104 q^{64} + 74 q^{66} + 164 q^{67} - 248 q^{69} + 12 q^{70} - 104 q^{71} + 252 q^{75} - 52 q^{77} + 404 q^{78} - 252 q^{80} + 216 q^{81} + 260 q^{82} + 284 q^{86} + 100 q^{88} + 88 q^{89} - 20 q^{91} - 296 q^{92} + 132 q^{93} + 204 q^{97} - 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.