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Properties

Label 1890.2.db
Level $1890$
Weight $2$
Character orbit 1890.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

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

Display 100 coefficients 10 coefficients

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

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