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Properties

Label 2016.3.fa
Level $2016$
Weight $3$
Character orbit 2016.fa
Rep. character $\chi_{2016}(43,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $4608$
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.fa (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 288 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 6176 4608 1568
Cusp forms 6112 4608 1504
Eisenstein series 64 0 64

Trace form

\( 4608 q + O(q^{10}) \) \( 4608 q - 192 q^{27} + 40 q^{30} - 464 q^{36} - 1008 q^{38} + 384 q^{39} + 104 q^{48} - 312 q^{50} - 360 q^{58} + 728 q^{60} + 720 q^{62} + 1664 q^{66} - 840 q^{72} - 624 q^{76} + 408 q^{78} + 1920 q^{80} + 1872 q^{86} - 896 q^{87} + 1320 q^{90} - 456 q^{92} + 1088 q^{96} + 512 q^{99} + O(q^{100}) \)

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

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