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Properties

Label 2112.2.ch
Level $2112$
Weight $2$
Character orbit 2112.ch
Rep. character $\chi_{2112}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $736$
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.ch (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 3200 800 2400
Cusp forms 2944 736 2208
Eisenstein series 256 64 192

Trace form

\( 736 q + 6 q^{3} + 24 q^{7} + O(q^{10}) \) \( 736 q + 6 q^{3} + 24 q^{7} - 12 q^{13} + 12 q^{19} - 4 q^{21} + 6 q^{27} - 16 q^{33} - 12 q^{37} + 12 q^{39} + 64 q^{43} + 4 q^{45} - 160 q^{49} + 18 q^{51} + 64 q^{55} - 12 q^{61} + 96 q^{67} + 12 q^{69} - 2 q^{75} - 12 q^{81} - 52 q^{85} + 32 q^{87} + 28 q^{91} - 18 q^{93} - 24 q^{97} - 42 q^{99} + O(q^{100}) \)

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

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