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Properties

Label 1850.2.bs
Level $1850$
Weight $2$
Character orbit 1850.bs
Rep. character $\chi_{1850}(71,\cdot)$
Character field $\Q(\zeta_{45})$
Dimension $2304$
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.bs (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{45})\)
Sturm bound: \(570\)

Dimensions

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

Total New Old
Modular forms 6912 2304 4608
Cusp forms 6720 2304 4416
Eisenstein series 192 0 192

Trace form

\( 2304 q + 12 q^{3} + 3 q^{5} + 6 q^{8} + 12 q^{9} + O(q^{10}) \) \( 2304 q + 12 q^{3} + 3 q^{5} + 6 q^{8} + 12 q^{9} + 12 q^{11} - 18 q^{12} + 12 q^{15} + 6 q^{17} - 12 q^{20} - 15 q^{25} - 162 q^{26} - 12 q^{27} + 96 q^{30} - 144 q^{31} + 12 q^{33} - 45 q^{34} - 6 q^{35} - 600 q^{36} + 24 q^{37} - 18 q^{40} + 126 q^{41} + 84 q^{42} - 210 q^{45} + 72 q^{46} - 18 q^{50} + 48 q^{53} - 84 q^{55} - 264 q^{57} + 42 q^{58} + 36 q^{59} - 132 q^{61} - 30 q^{62} + 288 q^{64} - 24 q^{65} - 126 q^{67} + 180 q^{69} + 12 q^{70} + 24 q^{71} + 36 q^{73} + 42 q^{74} - 444 q^{75} - 60 q^{77} + 12 q^{80} + 102 q^{81} - 48 q^{83} + 24 q^{84} + 108 q^{85} + 276 q^{87} - 24 q^{88} + 114 q^{89} + 177 q^{90} - 72 q^{91} + 36 q^{92} - 132 q^{93} + 12 q^{95} - 156 q^{97} + 24 q^{98} - 120 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)