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Properties

Label 1216.3.bg
Level $1216$
Weight $3$
Character orbit 1216.bg
Rep. character $\chi_{1216}(37,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2544$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.bg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1216 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1216, [\chi])\).

Total New Old
Modular forms 2576 2576 0
Cusp forms 2544 2544 0
Eisenstein series 32 32 0

Trace form

\( 2544 q - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{9} + O(q^{10}) \) \( 2544 q - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{17} - 8 q^{19} - 16 q^{20} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 416 q^{26} + 224 q^{28} - 16 q^{30} - 16 q^{35} - 16 q^{36} + 272 q^{38} - 16 q^{39} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{47} - 16 q^{49} - 1168 q^{54} - 16 q^{55} - 8 q^{57} - 16 q^{58} - 16 q^{61} - 32 q^{62} - 32 q^{63} - 208 q^{64} - 656 q^{66} + 224 q^{68} - 16 q^{73} - 16 q^{74} + 824 q^{76} - 16 q^{77} + 1760 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{87} - 16 q^{92} - 160 q^{93} - 288 q^{96} - 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.