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Properties

Label 2016.3.dp
Level $2016$
Weight $3$
Character orbit 2016.dp
Rep. character $\chi_{2016}(181,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1272$
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.dp (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2016, [\chi])\).

Total New Old
Modular forms 3104 1288 1816
Cusp forms 3040 1272 1768
Eisenstein series 64 16 48

Trace form

\( 1272 q + 8 q^{2} - 8 q^{4} - 4 q^{7} + 8 q^{8} + O(q^{10}) \) \( 1272 q + 8 q^{2} - 8 q^{4} - 4 q^{7} + 8 q^{8} + 8 q^{11} + 20 q^{14} - 4 q^{16} - 44 q^{22} + 72 q^{23} - 8 q^{25} + 56 q^{28} + 8 q^{29} + 8 q^{32} + 100 q^{35} - 8 q^{37} - 104 q^{43} - 204 q^{44} - 8 q^{46} - 304 q^{50} - 152 q^{53} - 356 q^{56} + 696 q^{58} - 464 q^{64} + 16 q^{65} - 40 q^{67} + 320 q^{70} + 520 q^{71} + 140 q^{74} + 4 q^{77} - 208 q^{85} + 8 q^{86} - 800 q^{88} - 196 q^{91} + 868 q^{92} + 16 q^{95} - 808 q^{98} + O(q^{100}) \)

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

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