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Properties

Label 1859.2.t
Level $1859$
Weight $2$
Character orbit 1859.t
Rep. character $\chi_{1859}(239,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1152$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.t (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 1568 1312 256
Cusp forms 1344 1152 192
Eisenstein series 224 160 64

Trace form

\( 1152 q + 10 q^{2} + 12 q^{3} + 6 q^{5} + 10 q^{6} + 10 q^{7} + 10 q^{8} - 236 q^{9} + O(q^{10}) \) \( 1152 q + 10 q^{2} + 12 q^{3} + 6 q^{5} + 10 q^{6} + 10 q^{7} + 10 q^{8} - 236 q^{9} - 8 q^{11} - 92 q^{14} - 10 q^{15} + 192 q^{16} + 10 q^{18} + 10 q^{19} - 4 q^{20} + 28 q^{22} + 50 q^{24} - 60 q^{27} + 10 q^{28} - 20 q^{29} - 18 q^{31} + 48 q^{33} - 44 q^{34} - 80 q^{35} + 18 q^{37} - 20 q^{40} - 50 q^{41} + 76 q^{42} + 14 q^{44} - 60 q^{45} - 50 q^{46} - 28 q^{47} - 36 q^{48} + 60 q^{50} - 24 q^{53} - 52 q^{55} + 10 q^{57} - 14 q^{58} - 4 q^{59} - 32 q^{60} - 60 q^{61} + 60 q^{63} - 204 q^{66} + 100 q^{67} + 140 q^{68} - 26 q^{71} - 170 q^{72} + 40 q^{73} + 20 q^{74} - 180 q^{79} + 82 q^{80} + 28 q^{81} + 110 q^{83} - 220 q^{84} - 30 q^{85} + 22 q^{86} - 48 q^{89} - 100 q^{92} - 60 q^{93} - 140 q^{94} + 160 q^{96} + 40 q^{97} - 70 q^{99} + O(q^{100}) \)

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

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