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Properties

Label 1890.2.bz
Level $1890$
Weight $2$
Character orbit 1890.bz
Rep. character $\chi_{1890}(73,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $192$
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.bz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1824 192 1632
Cusp forms 1632 192 1440
Eisenstein series 192 0 192

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 8 q^{11} - 192 q^{16} - 36 q^{17} - 8 q^{23} - 48 q^{35} + 12 q^{41} + 12 q^{46} + 16 q^{50} + 40 q^{53} + 4 q^{56} - 12 q^{58} - 16 q^{65} + 36 q^{68} - 16 q^{71} + 64 q^{77} - 168 q^{83} - 8 q^{86} - 8 q^{92} + 128 q^{95} + 48 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)