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Properties

Label 2016.2.fg
Level $2016$
Weight $2$
Character orbit 2016.fg
Rep. character $\chi_{2016}(19,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1264$
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.fg (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2016, [\chi])\).

Total New Old
Modular forms 3136 1296 1840
Cusp forms 3008 1264 1744
Eisenstein series 128 32 96

Trace form

\( 1264 q + 4 q^{2} - 4 q^{4} + 12 q^{5} - 8 q^{7} + 16 q^{8} + O(q^{10}) \) \( 1264 q + 4 q^{2} - 4 q^{4} + 12 q^{5} - 8 q^{7} + 16 q^{8} - 12 q^{10} + 4 q^{11} - 24 q^{14} - 8 q^{16} - 12 q^{19} - 8 q^{22} + 12 q^{23} - 4 q^{25} + 12 q^{26} + 12 q^{28} + 16 q^{29} + 4 q^{32} - 16 q^{35} - 4 q^{37} + 12 q^{38} - 12 q^{40} - 32 q^{43} + 44 q^{44} - 4 q^{46} + 24 q^{47} - 8 q^{50} - 84 q^{52} - 12 q^{53} + 48 q^{56} + 28 q^{58} + 108 q^{59} - 12 q^{61} + 56 q^{64} + 8 q^{65} + 4 q^{67} + 12 q^{68} + 28 q^{70} - 48 q^{71} - 12 q^{73} - 12 q^{74} + 8 q^{77} - 8 q^{79} + 48 q^{80} - 132 q^{82} + 24 q^{85} + 4 q^{86} - 48 q^{88} + 12 q^{89} - 56 q^{91} - 48 q^{92} - 84 q^{94} + 152 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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