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Properties

Label 1859.2.h
Level $1859$
Weight $2$
Character orbit 1859.h
Rep. character $\chi_{1859}(170,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $576$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 784 664 120
Cusp forms 672 576 96
Eisenstein series 112 88 24

Trace form

\( 576 q + 6 q^{2} + 6 q^{3} - 128 q^{4} + 6 q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 106 q^{9} + O(q^{10}) \) \( 576 q + 6 q^{2} + 6 q^{3} - 128 q^{4} + 6 q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 106 q^{9} + 8 q^{10} + 8 q^{11} - 20 q^{12} - 42 q^{14} - 2 q^{15} - 100 q^{16} + 6 q^{17} - 30 q^{18} - 10 q^{19} + 24 q^{20} - 20 q^{21} + 30 q^{22} + 28 q^{23} - 6 q^{24} - 86 q^{25} - 54 q^{27} - 42 q^{28} + 16 q^{29} + 64 q^{30} - 18 q^{31} - 48 q^{32} + 12 q^{33} - 20 q^{34} - 20 q^{35} - 98 q^{36} - 6 q^{37} + 32 q^{38} - 114 q^{40} + 26 q^{41} - 38 q^{42} + 48 q^{43} - 66 q^{44} - 60 q^{45} + 2 q^{46} + 32 q^{47} + 54 q^{48} - 66 q^{49} + 8 q^{50} + 42 q^{51} - 36 q^{53} + 76 q^{54} - 26 q^{55} + 140 q^{56} - 18 q^{57} + 18 q^{58} - 16 q^{59} + 28 q^{60} - 6 q^{61} - 70 q^{62} + 24 q^{63} - 88 q^{64} - 6 q^{66} + 28 q^{67} + 172 q^{68} + 8 q^{69} + 8 q^{70} + 14 q^{71} - 6 q^{72} + 12 q^{73} - 32 q^{74} - 6 q^{75} + 4 q^{76} - 34 q^{77} - 82 q^{79} + 2 q^{80} - 58 q^{81} + 114 q^{82} + 46 q^{83} + 148 q^{84} - 22 q^{85} - 26 q^{86} + 56 q^{87} + 50 q^{88} + 240 q^{90} - 32 q^{92} - 20 q^{93} - 50 q^{94} - 78 q^{95} + 48 q^{96} + 44 q^{97} - 156 q^{98} - 46 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1859, [\chi])\) into lower level spaces

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