Properties

Label 2016.2.do
Level 2016
Weight 2
Character orbit do
Rep. character \(\chi_{2016}(323,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 384
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.do (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 96 \)
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 384 1184
Cusp forms 1504 384 1120
Eisenstein series 64 0 64

Trace form

\( 384q + O(q^{10}) \) \( 384q - 32q^{10} - 16q^{16} - 64q^{22} + 128q^{46} + 128q^{52} + 128q^{55} - 128q^{61} + 32q^{67} + 96q^{70} + 32q^{76} + 128q^{79} - 160q^{88} - 192q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database