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Properties

Label 1890.2.di
Level $1890$
Weight $2$
Character orbit 1890.di
Rep. character $\chi_{1890}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1728$
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.di (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 945 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 5280 1728 3552
Cusp forms 5088 1728 3360
Eisenstein series 192 0 192

Trace form

\( 1728 q + O(q^{10}) \) \( 1728 q - 24 q^{11} - 24 q^{23} + 144 q^{30} - 36 q^{35} - 24 q^{36} + 48 q^{42} - 96 q^{50} + 240 q^{53} + 12 q^{56} - 72 q^{57} + 84 q^{63} + 24 q^{65} + 48 q^{72} - 240 q^{77} + 24 q^{78} + 24 q^{81} + 48 q^{92} + 144 q^{93} + O(q^{100}) \)

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

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