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Properties

Label 2112.2.bt
Level $2112$
Weight $2$
Character orbit 2112.bt
Rep. character $\chi_{2112}(191,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $368$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2112.bt (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 132 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).

Total New Old
Modular forms 1632 400 1232
Cusp forms 1440 368 1072
Eisenstein series 192 32 160

Trace form

\( 368 q - 6 q^{9} + O(q^{10}) \) \( 368 q - 6 q^{9} + 12 q^{13} + 28 q^{21} + 64 q^{25} + 6 q^{33} + 12 q^{37} - 60 q^{45} + 56 q^{49} - 34 q^{57} + 12 q^{61} - 12 q^{73} - 22 q^{81} + 52 q^{85} - 6 q^{93} - 44 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)