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Properties

Label 1850.2.cb
Level $1850$
Weight $2$
Character orbit 1850.cb
Rep. character $\chi_{1850}(139,\cdot)$
Character field $\Q(\zeta_{90})$
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.cb (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{90})\)
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

\( 2304 q - 3 q^{5} + 12 q^{9} + O(q^{10}) \) \( 2304 q - 3 q^{5} + 12 q^{9} - 12 q^{11} + 30 q^{12} - 12 q^{15} - 12 q^{20} + 33 q^{25} - 126 q^{26} + 96 q^{30} + 45 q^{34} - 6 q^{35} + 600 q^{36} - 18 q^{40} - 90 q^{41} - 54 q^{45} - 72 q^{46} - 42 q^{50} + 84 q^{55} - 108 q^{59} + 12 q^{61} + 90 q^{62} + 288 q^{64} + 60 q^{65} - 30 q^{67} + 180 q^{69} + 12 q^{70} - 96 q^{71} + 42 q^{74} - 324 q^{75} + 210 q^{81} - 24 q^{84} - 108 q^{85} + 300 q^{87} - 114 q^{89} - 177 q^{90} - 72 q^{91} + 60 q^{92} + 144 q^{95} + 120 q^{99} + O(q^{100}) \)

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

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