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Properties

Label 1666.2.bi
Level $1666$
Weight $2$
Character orbit 1666.bi
Rep. character $\chi_{1666}(27,\cdot)$
Character field $\Q(\zeta_{112})$
Dimension $4032$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1666.bi (of order \(112\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{112})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1666, [\chi])\).

Total New Old
Modular forms 12288 4032 8256
Cusp forms 11904 4032 7872
Eisenstein series 384 0 384

Trace form

\( 4032 q + O(q^{10}) \) \( 4032 q - 80 q^{11} + 16 q^{14} - 96 q^{15} + 64 q^{18} + 48 q^{21} - 32 q^{22} + 32 q^{25} - 32 q^{35} + 64 q^{37} + 48 q^{42} - 384 q^{49} + 96 q^{63} - 224 q^{69} + 64 q^{71} + 336 q^{75} + 16 q^{77} - 320 q^{78} + 192 q^{85} - 64 q^{91} + 32 q^{92} + 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1666, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)