Properties

Label 2016.2.bz
Level $2016$
Weight $2$
Character orbit 2016.bz
Rep. character $\chi_{2016}(239,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.bz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2016, [\chi])\).

Total New Old
Modular forms 800 144 656
Cusp forms 736 144 592
Eisenstein series 64 0 64

Trace form

\( 144 q + O(q^{10}) \) \( 144 q - 72 q^{25} - 24 q^{27} - 16 q^{33} + 24 q^{41} + 72 q^{49} + 8 q^{57} + 72 q^{59} + 112 q^{75} - 8 q^{81} + 64 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)