Properties

Label 2016.2.dk
Level 2016
Weight 2
Character orbit dk
Rep. character \(\chi_{2016}(125,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 512
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.dk (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 672 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1568 512 1056
Cusp forms 1504 512 992
Eisenstein series 64 0 64

Trace form

\( 512q + O(q^{10}) \) \( 512q + 16q^{16} + 128q^{58} + 192q^{64} - 32q^{67} + 96q^{91} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database