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Properties

Label 2112.2.da
Level $2112$
Weight $2$
Character orbit 2112.da
Rep. character $\chi_{2112}(37,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $6144$
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.da (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 704 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 12416 6144 6272
Cusp forms 12160 6144 6016
Eisenstein series 256 0 256

Trace form

\( 6144 q + O(q^{10}) \) \( 6144 q + 16 q^{22} - 240 q^{26} + 160 q^{32} + 160 q^{34} + 160 q^{40} + 16 q^{44} - 96 q^{52} + 64 q^{55} - 224 q^{56} + 128 q^{59} - 96 q^{60} + 64 q^{63} + 288 q^{64} - 96 q^{66} + 64 q^{67} - 96 q^{70} + 128 q^{71} - 224 q^{74} - 192 q^{75} - 96 q^{78} + 80 q^{88} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 2}\)