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Properties

Label 1850.2.bg
Level $1850$
Weight $2$
Character orbit 1850.bg
Rep. character $\chi_{1850}(117,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $760$
Sturm bound $570$

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Defining parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.bg (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(570\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1850, [\chi])\).

Total New Old
Modular forms 2312 760 1552
Cusp forms 2248 760 1488
Eisenstein series 64 0 64

Trace form

\( 760 q + 2 q^{2} - 8 q^{3} - 190 q^{4} - 14 q^{5} + 2 q^{8} + O(q^{10}) \) \( 760 q + 2 q^{2} - 8 q^{3} - 190 q^{4} - 14 q^{5} + 2 q^{8} - 2 q^{10} - 8 q^{12} + 8 q^{13} + 8 q^{15} - 190 q^{16} - 4 q^{20} - 40 q^{22} + 8 q^{23} - 10 q^{25} + 40 q^{27} - 10 q^{29} - 8 q^{32} + 8 q^{35} + 8 q^{37} - 2 q^{40} + 64 q^{43} + 76 q^{45} + 8 q^{47} + 32 q^{48} + 10 q^{50} + 8 q^{52} + 96 q^{53} + 8 q^{55} + 112 q^{57} + 18 q^{58} - 20 q^{59} - 12 q^{60} + 90 q^{61} + 40 q^{62} - 190 q^{64} - 24 q^{65} - 16 q^{67} - 60 q^{69} - 16 q^{70} - 2 q^{73} - 10 q^{74} - 248 q^{75} + 120 q^{77} + 20 q^{78} + 6 q^{80} + 110 q^{81} - 20 q^{83} + 100 q^{87} + 20 q^{89} + 40 q^{90} - 12 q^{92} + 168 q^{93} - 40 q^{95} + 60 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1850, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \)