Properties

Label 2016.2.dm
Level 2016
Weight 2
Character orbit dm
Rep. character \(\chi_{2016}(253,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 480
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.dm (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 32 \)
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 480 1088
Cusp forms 1504 480 1024
Eisenstein series 64 0 64

Trace form

\( 480q + O(q^{10}) \) \( 480q + 16q^{10} - 4q^{16} + 36q^{22} - 8q^{23} + 40q^{26} + 40q^{32} + 40q^{34} + 56q^{38} + 40q^{40} - 8q^{43} + 4q^{44} + 64q^{46} + 104q^{50} + 64q^{52} - 16q^{53} - 64q^{55} + 28q^{56} + 72q^{58} + 64q^{61} + 72q^{62} + 8q^{67} - 8q^{68} - 48q^{70} + 28q^{74} - 32q^{76} - 16q^{77} - 144q^{80} - 80q^{82} - 168q^{86} - 80q^{88} - 156q^{92} - 152q^{94} + 128q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database