Properties

Label 1890.2.db
Level 1890
Weight 2
Character orbit db
Rep. character \(\chi_{1890}(209,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 864
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.db (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 945 \)
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 864 1776
Cusp forms 2544 864 1680
Eisenstein series 96 0 96

Trace form

\(864q \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(864q \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 72q^{30} \) \(\mathstrut +\mathstrut 54q^{35} \) \(\mathstrut -\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 132q^{39} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 36q^{50} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 36q^{60} \) \(\mathstrut -\mathstrut 432q^{64} \) \(\mathstrut +\mathstrut 72q^{65} \) \(\mathstrut +\mathstrut 72q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut +\mathstrut 120q^{95} \) \(\mathstrut -\mathstrut 72q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

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