Properties

Label 1890.2.cs
Level 1890
Weight 2
Character orbit cs
Rep. character \(\chi_{1890}(41,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 576
Sturm bound 864

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Defining parameters

Level: \( N \) = \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1890.cs (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).

Total New Old
Modular forms 2640 576 2064
Cusp forms 2544 576 1968
Eisenstein series 96 0 96

Trace form

\( 576q + 12q^{9} + O(q^{10}) \) \( 576q + 12q^{9} - 12q^{11} - 6q^{14} + 24q^{21} + 144q^{23} - 12q^{29} + 12q^{36} + 12q^{39} - 18q^{49} + 72q^{51} - 6q^{56} + 48q^{57} + 72q^{63} + 288q^{64} + 24q^{65} - 36q^{70} + 144q^{71} + 72q^{74} + 12q^{77} + 96q^{78} + 72q^{79} + 12q^{81} - 12q^{84} + 72q^{85} + 96q^{86} + 36q^{91} - 72q^{92} + 96q^{93} - 72q^{98} - 216q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)