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Properties

Label 1859.2.e
Level $1859$
Weight $2$
Character orbit 1859.e
Rep. character $\chi_{1859}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $256$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 392 256 136
Cusp forms 336 256 80
Eisenstein series 56 0 56

Trace form

\( 256 q + 2 q^{2} + 2 q^{3} - 128 q^{4} + 8 q^{5} - 6 q^{6} + 2 q^{7} - 126 q^{9} + O(q^{10}) \) \( 256 q + 2 q^{2} + 2 q^{3} - 128 q^{4} + 8 q^{5} - 6 q^{6} + 2 q^{7} - 126 q^{9} - 6 q^{10} + 4 q^{12} - 8 q^{14} + 16 q^{15} - 132 q^{16} - 8 q^{17} - 28 q^{18} - 2 q^{19} - 14 q^{20} + 20 q^{21} + 2 q^{22} + 10 q^{23} - 12 q^{24} + 264 q^{25} - 40 q^{27} + 2 q^{28} + 16 q^{30} - 4 q^{31} + 22 q^{32} + 4 q^{34} + 32 q^{35} - 110 q^{36} - 10 q^{37} - 40 q^{38} + 76 q^{40} - 20 q^{41} + 20 q^{42} - 14 q^{43} + 8 q^{44} - 14 q^{45} - 38 q^{46} + 48 q^{47} + 2 q^{48} - 138 q^{49} + 26 q^{50} + 4 q^{51} - 16 q^{53} - 32 q^{54} + 8 q^{55} + 16 q^{56} - 16 q^{57} + 24 q^{58} + 16 q^{59} - 100 q^{60} - 30 q^{61} + 12 q^{62} + 6 q^{63} + 284 q^{64} - 56 q^{66} + 6 q^{67} - 18 q^{69} + 84 q^{70} + 10 q^{71} + 68 q^{72} + 20 q^{73} - 46 q^{74} + 6 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{79} - 48 q^{80} - 136 q^{81} + 34 q^{82} + 44 q^{83} - 16 q^{84} + 36 q^{85} + 76 q^{86} - 6 q^{88} + 10 q^{89} + 40 q^{90} - 120 q^{92} + 70 q^{93} + 2 q^{94} + 16 q^{95} - 80 q^{96} + 14 q^{97} - 56 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1859, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)