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Properties

Label 2016.3.bi
Level $2016$
Weight $3$
Character orbit 2016.bi
Rep. character $\chi_{2016}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
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 392 1176
Cusp forms 1504 376 1128
Eisenstein series 64 16 48

Trace form

\( 376 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \) \( 376 q + 2 q^{3} - 2 q^{9} + 4 q^{11} - 4 q^{17} + 4 q^{19} - 1724 q^{25} + 8 q^{27} - 74 q^{33} - 42 q^{35} - 4 q^{41} + 4 q^{43} - 2 q^{49} - 194 q^{51} + 28 q^{57} - 2 q^{59} + 102 q^{65} - 2 q^{67} - 4 q^{73} + 24 q^{75} + 14 q^{81} + 244 q^{83} - 52 q^{89} + 204 q^{91} - 4 q^{97} + 170 q^{99} + O(q^{100}) \)

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

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