Properties

Label 2016.2.dq
Level 2016
Weight 2
Character orbit dq
Rep. character \(\chi_{2016}(307,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 632
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.dq (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 224 \)
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 648 920
Cusp forms 1504 632 872
Eisenstein series 64 16 48

Trace form

\( 632q + 8q^{2} - 8q^{4} - 4q^{7} + 8q^{8} + O(q^{10}) \) \( 632q + 8q^{2} - 8q^{4} - 4q^{7} + 8q^{8} + 8q^{11} - 12q^{14} - 4q^{16} - 4q^{22} - 8q^{25} - 24q^{28} + 8q^{29} + 8q^{32} + 28q^{35} - 8q^{37} - 16q^{43} + 100q^{44} - 8q^{46} + 32q^{50} + 24q^{53} - 36q^{56} + 56q^{58} - 80q^{64} + 16q^{65} - 16q^{67} - 40q^{70} + 72q^{71} - 108q^{74} + 4q^{77} - 16q^{79} - 48q^{85} + 8q^{86} - 96q^{88} + 44q^{91} + 84q^{92} - 56q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database