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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) into irreducible Hecke orbits

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

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