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Properties

Label 1850.2.ca
Level $1850$
Weight $2$
Character orbit 1850.ca
Rep. character $\chi_{1850}(21,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2256$
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.ca (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 6960 2256 4704
Cusp forms 6768 2256 4512
Eisenstein series 192 0 192

Trace form

\( 2256 q - 12 q^{3} + 12 q^{9} + O(q^{10}) \) \( 2256 q - 12 q^{3} + 12 q^{9} + 12 q^{11} - 18 q^{12} + 18 q^{25} + 156 q^{26} + 12 q^{27} + 96 q^{30} - 12 q^{33} - 30 q^{35} + 540 q^{36} - 24 q^{37} - 12 q^{40} + 120 q^{41} + 84 q^{42} - 54 q^{45} + 72 q^{46} + 36 q^{50} + 24 q^{53} - 60 q^{55} + 312 q^{57} - 12 q^{58} - 108 q^{59} - 72 q^{61} + 30 q^{62} - 282 q^{64} - 42 q^{65} - 126 q^{67} - 180 q^{69} + 12 q^{70} - 24 q^{71} + 24 q^{73} + 12 q^{74} - 444 q^{75} + 60 q^{77} - 90 q^{81} + 48 q^{83} - 24 q^{84} - 276 q^{87} + 72 q^{88} + 96 q^{89} - 162 q^{90} + 72 q^{91} + 36 q^{92} - 36 q^{93} + 48 q^{95} - 144 q^{97} - 24 q^{98} - 120 q^{99} + O(q^{100}) \)

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

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