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Properties

Label 2016.2.dg
Level $2016$
Weight $2$
Character orbit 2016.dg
Rep. character $\chi_{2016}(1103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $184$
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.dg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
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 800 200 600
Cusp forms 736 184 552
Eisenstein series 64 16 48

Trace form

\( 184 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \) \( 184 q + 2 q^{3} - 2 q^{9} + 4 q^{19} + 148 q^{25} + 8 q^{27} + 22 q^{33} + 30 q^{35} - 12 q^{41} + 4 q^{43} - 2 q^{49} - 26 q^{51} + 4 q^{57} + 6 q^{59} - 6 q^{65} - 2 q^{67} - 4 q^{73} + 36 q^{75} - 10 q^{81} + 72 q^{83} + 24 q^{89} + 36 q^{91} - 4 q^{97} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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