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Properties

Label 1216.3.by
Level $1216$
Weight $3$
Character orbit 1216.by
Rep. character $\chi_{1216}(69,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $5088$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.by (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1216 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 5152 5152 0
Cusp forms 5088 5088 0
Eisenstein series 64 64 0

Trace form

\( 5088 q - 24 q^{2} - 24 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 32 q^{7} - 8 q^{9} + O(q^{10}) \) \( 5088 q - 24 q^{2} - 24 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 32 q^{7} - 8 q^{9} - 24 q^{10} - 32 q^{11} - 24 q^{13} - 24 q^{14} - 24 q^{15} - 8 q^{16} - 8 q^{17} - 16 q^{19} - 32 q^{20} - 24 q^{21} - 24 q^{22} - 8 q^{23} - 8 q^{24} - 8 q^{25} + 368 q^{26} - 248 q^{28} - 24 q^{29} - 32 q^{30} - 24 q^{32} - 384 q^{34} - 8 q^{35} - 8 q^{36} + 544 q^{38} - 32 q^{39} - 1104 q^{40} - 24 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} - 32 q^{45} - 8 q^{47} - 24 q^{48} - 32 q^{49} - 1176 q^{51} - 24 q^{52} - 24 q^{53} - 584 q^{54} - 8 q^{55} - 16 q^{57} - 32 q^{58} - 24 q^{59} - 24 q^{60} - 8 q^{61} - 88 q^{62} - 16 q^{63} + 160 q^{64} + 632 q^{66} - 24 q^{67} + 448 q^{68} - 2040 q^{70} - 24 q^{71} - 24 q^{72} - 8 q^{73} - 8 q^{74} - 848 q^{76} - 32 q^{77} - 24 q^{78} - 24 q^{79} - 1784 q^{80} - 8 q^{81} - 8 q^{82} - 32 q^{83} - 8 q^{85} - 24 q^{86} - 32 q^{87} - 24 q^{89} - 2184 q^{90} - 24 q^{91} - 8 q^{92} - 80 q^{93} - 576 q^{96} - 24 q^{98} + 136 q^{99} + O(q^{100}) \)

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.