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Properties

Label 1216.4.bx
Level $1216$
Weight $4$
Character orbit 1216.bx
Rep. character $\chi_{1216}(45,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $7648$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.bx (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1216 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1216, [\chi])\).

Total New Old
Modular forms 7712 7712 0
Cusp forms 7648 7648 0
Eisenstein series 64 64 0

Trace form

\( 7648 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 32 q^{7} - 32 q^{8} - 8 q^{9} + O(q^{10}) \) \( 7648 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 32 q^{7} - 32 q^{8} - 8 q^{9} - 8 q^{10} - 32 q^{11} - 32 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 32 q^{18} - 16 q^{19} - 32 q^{20} - 8 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} - 8 q^{25} + 48 q^{26} - 32 q^{27} + 1512 q^{28} - 8 q^{29} - 32 q^{30} + 2472 q^{32} - 1008 q^{34} - 8 q^{35} - 8 q^{36} - 32 q^{37} + 864 q^{38} - 32 q^{39} + 1632 q^{40} - 8 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} - 32 q^{45} - 32 q^{46} - 8 q^{47} - 8 q^{48} - 32 q^{49} - 11456 q^{50} + 2968 q^{51} - 8 q^{52} - 8 q^{53} - 1736 q^{54} - 8 q^{55} - 32 q^{56} - 16 q^{57} - 32 q^{58} - 8 q^{59} - 9800 q^{60} - 8 q^{61} - 2872 q^{62} - 16 q^{63} - 12128 q^{64} - 64 q^{65} - 11080 q^{66} - 8 q^{67} + 4096 q^{68} - 32 q^{69} + 2008 q^{70} - 8 q^{71} - 8 q^{72} - 8 q^{73} - 8 q^{74} - 32 q^{75} + 5936 q^{76} - 32 q^{77} - 8 q^{78} - 11336 q^{79} + 744 q^{80} - 8 q^{81} - 8 q^{82} - 32 q^{83} - 32 q^{84} - 8 q^{85} - 8 q^{86} - 32 q^{87} + 6208 q^{88} - 8 q^{89} - 9368 q^{90} - 8 q^{91} - 8 q^{92} + 208 q^{93} + 17824 q^{94} - 51712 q^{96} + 24200 q^{98} - 440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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