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Properties

Label 2016.3.bp
Level $2016$
Weight $3$
Character orbit 2016.bp
Rep. character $\chi_{2016}(383,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $384$
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.bp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1568 384 1184
Cusp forms 1504 384 1120
Eisenstein series 64 0 64

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 16 q^{21} - 960 q^{25} - 144 q^{29} - 240 q^{45} - 32 q^{57} + 288 q^{77} - 256 q^{81} - 432 q^{89} + 160 q^{93} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)