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Properties

Label 2016.3.dr
Level $2016$
Weight $3$
Character orbit 2016.dr
Rep. character $\chi_{2016}(197,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $768$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2016.dr (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2016, [\chi])\).

Total New Old
Modular forms 3104 768 2336
Cusp forms 3040 768 2272
Eisenstein series 64 0 64

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 160 q^{10} - 16 q^{16} - 448 q^{22} - 128 q^{46} + 640 q^{52} - 1024 q^{55} + 256 q^{61} + 128 q^{67} + 672 q^{70} + 416 q^{76} + 1120 q^{88} + 192 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)