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Properties

Label 1859.2.bh
Level $1859$
Weight $2$
Character orbit 1859.bh
Rep. character $\chi_{1859}(56,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $3600$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.bh (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 4416 3600 816
Cusp forms 4320 3600 720
Eisenstein series 96 0 96

Trace form

\( 3600 q - 2 q^{3} - 146 q^{4} + 18 q^{6} + 6 q^{7} + 144 q^{9} + O(q^{10}) \) \( 3600 q - 2 q^{3} - 146 q^{4} + 18 q^{6} + 6 q^{7} + 144 q^{9} - 4 q^{10} - 20 q^{12} + 26 q^{13} + 24 q^{14} + 104 q^{15} + 142 q^{16} + 6 q^{17} - 156 q^{18} + 6 q^{19} + 24 q^{22} - 138 q^{23} - 120 q^{24} + 288 q^{25} - 20 q^{26} - 8 q^{27} - 18 q^{28} - 2 q^{29} - 112 q^{30} - 10 q^{32} - 132 q^{36} + 36 q^{37} - 138 q^{38} - 96 q^{39} + 172 q^{40} - 30 q^{41} - 520 q^{42} - 6 q^{43} - 130 q^{45} - 6 q^{46} - 130 q^{47} + 72 q^{48} - 152 q^{49} - 54 q^{50} + 142 q^{51} - 2 q^{52} + 90 q^{53} - 252 q^{54} - 8 q^{55} + 32 q^{56} + 134 q^{58} - 160 q^{59} - 8 q^{61} + 24 q^{62} - 90 q^{63} + 272 q^{64} - 2 q^{65} + 16 q^{66} - 6 q^{67} + 72 q^{68} - 2 q^{69} - 6 q^{71} - 18 q^{72} - 56 q^{74} + 208 q^{75} + 24 q^{76} - 16 q^{77} - 48 q^{78} - 32 q^{79} - 66 q^{80} + 126 q^{81} + 84 q^{82} + 506 q^{84} + 72 q^{85} - 32 q^{87} - 6 q^{88} - 30 q^{89} - 76 q^{90} + 146 q^{91} + 136 q^{92} - 62 q^{93} - 18 q^{94} - 8 q^{95} - 18 q^{97} + 66 q^{98} + O(q^{100}) \)

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

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