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Properties

Label 1216.2.bw
Level $1216$
Weight $2$
Character orbit 1216.bw
Rep. character $\chi_{1216}(27,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $2528$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.bw (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1216 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1216, [\chi])\).

Total New Old
Modular forms 2592 2592 0
Cusp forms 2528 2528 0
Eisenstein series 64 64 0

Trace form

\( 2528 q - 24 q^{2} - 24 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 32 q^{7} - 8 q^{9} + O(q^{10}) \) \( 2528 q - 24 q^{2} - 24 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 32 q^{7} - 8 q^{9} - 24 q^{10} - 32 q^{11} - 24 q^{13} - 24 q^{14} - 24 q^{15} - 8 q^{16} - 8 q^{17} - 16 q^{19} - 32 q^{20} - 24 q^{21} - 24 q^{22} - 8 q^{23} - 8 q^{24} - 8 q^{25} - 112 q^{26} + 72 q^{28} - 24 q^{29} - 32 q^{30} - 24 q^{32} - 144 q^{34} - 8 q^{35} - 8 q^{36} + 64 q^{38} - 32 q^{39} - 144 q^{40} - 24 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} - 32 q^{45} - 8 q^{47} - 24 q^{48} - 32 q^{49} + 72 q^{51} - 24 q^{52} - 24 q^{53} + 56 q^{54} - 8 q^{55} - 16 q^{57} - 32 q^{58} - 24 q^{59} - 24 q^{60} - 8 q^{61} + 56 q^{62} + 160 q^{64} + 216 q^{66} - 24 q^{67} + 64 q^{68} - 312 q^{70} - 24 q^{71} - 24 q^{72} - 8 q^{73} - 8 q^{74} - 80 q^{76} - 32 q^{77} - 24 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} - 8 q^{82} - 32 q^{83} - 8 q^{85} - 24 q^{86} - 32 q^{87} - 24 q^{89} + 408 q^{90} - 24 q^{91} - 8 q^{92} + 16 q^{93} - 32 q^{95} - 576 q^{96} - 24 q^{98} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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