Properties

Label 1890.2.bt
Level 1890
Weight 2
Character orbit bt
Rep. character \(\chi_{1890}(331,\cdot)\)
Character field \(\Q(\zeta_{9})\)
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.bt (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{9})\)
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

\( 576q - 6q^{6} - 24q^{9} + O(q^{10}) \) \( 576q - 6q^{6} - 24q^{9} - 24q^{11} + 6q^{14} + 48q^{17} + 24q^{21} - 36q^{23} - 6q^{29} + 72q^{33} - 6q^{36} + 12q^{39} + 12q^{41} - 6q^{45} - 36q^{47} - 36q^{49} + 72q^{51} + 72q^{54} + 6q^{56} + 48q^{57} + 120q^{59} - 18q^{61} + 96q^{62} + 36q^{63} - 288q^{64} + 12q^{65} + 108q^{69} + 18q^{70} - 48q^{71} - 144q^{73} + 72q^{74} + 60q^{77} - 96q^{78} + 36q^{79} + 12q^{80} - 24q^{81} + 6q^{84} - 72q^{85} + 48q^{86} + 120q^{87} - 72q^{91} - 36q^{92} + 48q^{93} + 36q^{94} + 48q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database