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Properties

Label 1216.2.ch
Level $1216$
Weight $2$
Character orbit 1216.ch
Rep. character $\chi_{1216}(3,\cdot)$
Character field $\Q(\zeta_{144})$
Dimension $7584$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.ch (of order \(144\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1216 \)
Character field: \(\Q(\zeta_{144})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 7776 7776 0
Cusp forms 7584 7584 0
Eisenstein series 192 192 0

Trace form

\( 7584 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 48 q^{6} - 24 q^{7} - 72 q^{8} - 48 q^{9} + O(q^{10}) \) \( 7584 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 48 q^{6} - 24 q^{7} - 72 q^{8} - 48 q^{9} - 48 q^{10} - 24 q^{11} - 72 q^{12} - 48 q^{13} - 48 q^{14} - 48 q^{15} - 48 q^{16} - 48 q^{17} - 48 q^{19} - 96 q^{20} - 48 q^{21} - 48 q^{22} - 48 q^{23} - 48 q^{24} - 48 q^{25} - 24 q^{26} - 72 q^{27} - 48 q^{28} - 48 q^{29} - 24 q^{30} - 144 q^{31} - 48 q^{32} - 288 q^{34} - 48 q^{35} - 48 q^{36} - 168 q^{38} - 96 q^{39} + 72 q^{40} - 48 q^{41} - 48 q^{42} - 48 q^{43} - 48 q^{44} - 24 q^{45} - 72 q^{46} - 48 q^{47} - 48 q^{48} - 24 q^{49} + 144 q^{50} - 144 q^{51} - 48 q^{52} - 48 q^{53} - 240 q^{54} - 48 q^{55} - 48 q^{57} - 96 q^{58} - 48 q^{59} - 48 q^{60} - 48 q^{61} - 96 q^{62} - 24 q^{64} - 144 q^{65} - 48 q^{66} - 48 q^{67} - 168 q^{68} - 72 q^{69} + 240 q^{70} - 48 q^{71} - 48 q^{72} - 48 q^{73} - 48 q^{74} - 48 q^{76} - 96 q^{77} - 48 q^{78} - 48 q^{79} - 48 q^{80} - 48 q^{81} - 48 q^{82} - 24 q^{83} - 72 q^{84} - 48 q^{85} - 48 q^{86} - 24 q^{87} - 72 q^{88} - 48 q^{89} - 480 q^{90} - 48 q^{91} - 48 q^{92} - 120 q^{93} - 96 q^{95} + 720 q^{96} - 48 q^{98} - 48 q^{99} + O(q^{100}) \)

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.