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Properties

Label 2112.2.x
Level $2112$
Weight $2$
Character orbit 2112.x
Rep. character $\chi_{2112}(593,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 800 200 600
Cusp forms 736 184 552
Eisenstein series 64 16 48

Trace form

\( 184 q + 4 q^{3} + O(q^{10}) \) \( 184 q + 4 q^{3} + 8 q^{15} + 4 q^{27} + 16 q^{31} - 4 q^{33} - 8 q^{37} - 24 q^{45} + 120 q^{49} + 72 q^{67} - 16 q^{69} - 28 q^{75} - 8 q^{81} + 16 q^{91} - 16 q^{93} - 16 q^{97} + 52 q^{99} + O(q^{100}) \)

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

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