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Properties

Label 2016.3.dl
Level $2016$
Weight $3$
Character orbit 2016.dl
Rep. character $\chi_{2016}(379,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $960$
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.dl (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
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 960 2144
Cusp forms 3040 960 2080
Eisenstein series 64 0 64

Trace form

\( 960 q + O(q^{10}) \) \( 960 q - 80 q^{10} - 4 q^{16} + 188 q^{22} + 64 q^{23} - 200 q^{26} + 40 q^{32} + 120 q^{34} - 504 q^{38} + 360 q^{40} - 96 q^{43} + 52 q^{44} - 64 q^{46} + 312 q^{50} + 320 q^{52} + 160 q^{53} + 512 q^{55} - 196 q^{56} - 360 q^{58} - 128 q^{61} + 312 q^{62} + 32 q^{67} + 856 q^{68} - 336 q^{70} + 308 q^{74} + 608 q^{76} - 224 q^{77} - 1024 q^{79} + 880 q^{80} - 240 q^{82} + 488 q^{86} + 560 q^{88} + 532 q^{92} - 744 q^{94} + O(q^{100}) \)

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

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