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Properties

Label 2016.2.be
Level $2016$
Weight $2$
Character orbit 2016.be
Rep. character $\chi_{2016}(1201,\cdot)$
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.be (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

\( 184 q + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 184 q + 2 q^{7} - 2 q^{9} + 2 q^{15} - 4 q^{17} + 4 q^{23} - 156 q^{25} - 2 q^{31} + 22 q^{33} + 14 q^{39} - 4 q^{41} - 42 q^{47} - 2 q^{49} - 4 q^{55} - 20 q^{57} - 50 q^{63} + 22 q^{65} + 16 q^{71} - 4 q^{73} - 2 q^{79} + 6 q^{81} - 4 q^{87} + 4 q^{89} - 22 q^{95} - 4 q^{97} + O(q^{100}) \)

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

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