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Properties

Label 1859.2.ba
Level $1859$
Weight $2$
Character orbit 1859.ba
Rep. character $\chi_{1859}(100,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $3648$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.ba (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 4416 3648 768
Cusp forms 4320 3648 672
Eisenstein series 96 0 96

Trace form

\( 3648 q + 2 q^{2} + 2 q^{3} + 152 q^{4} + 8 q^{5} - 6 q^{6} + 2 q^{7} + 154 q^{9} + O(q^{10}) \) \( 3648 q + 2 q^{2} + 2 q^{3} + 152 q^{4} + 8 q^{5} - 6 q^{6} + 2 q^{7} + 154 q^{9} - 6 q^{10} + 4 q^{12} - 16 q^{13} - 8 q^{14} - 88 q^{15} + 148 q^{16} - 8 q^{17} + 128 q^{18} - 2 q^{19} - 14 q^{20} + 20 q^{21} - 24 q^{22} - 154 q^{23} - 168 q^{24} - 280 q^{25} - 2 q^{26} + 8 q^{27} + 2 q^{28} - 8 q^{29} - 112 q^{30} - 4 q^{31} - 264 q^{32} + 4 q^{34} + 150 q^{36} - 10 q^{37} - 130 q^{38} - 120 q^{39} - 158 q^{40} - 20 q^{41} + 496 q^{42} - 22 q^{43} + 8 q^{44} - 144 q^{45} - 38 q^{46} - 82 q^{47} - 96 q^{48} + 142 q^{49} + 26 q^{50} - 78 q^{51} - 22 q^{52} - 156 q^{53} + 280 q^{54} + 8 q^{55} - 4 q^{56} - 16 q^{57} - 80 q^{58} + 224 q^{59} - 100 q^{60} - 30 q^{61} - 36 q^{62} + 6 q^{63} - 228 q^{64} + 24 q^{65} - 16 q^{66} - 202 q^{67} - 154 q^{68} - 18 q^{69} - 124 q^{70} + 10 q^{71} + 68 q^{72} + 20 q^{73} - 252 q^{74} - 200 q^{75} + 16 q^{76} - 16 q^{77} - 60 q^{78} + 32 q^{79} - 48 q^{80} + 144 q^{81} - 6 q^{82} + 44 q^{83} - 510 q^{84} - 276 q^{85} + 76 q^{86} - 16 q^{87} - 6 q^{88} + 10 q^{89} + 88 q^{90} - 150 q^{91} + 32 q^{92} + 174 q^{93} - 14 q^{94} - 24 q^{95} - 80 q^{96} + 14 q^{97} - 56 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1859, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)