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Properties

Label 608.4.bt
Level $608$
Weight $4$
Character orbit 608.bt
Rep. character $\chi_{608}(3,\cdot)$
Character field $\Q(\zeta_{72})$
Dimension $5712$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 608.bt (of order \(72\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 608 \)
Character field: \(\Q(\zeta_{72})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(608, [\chi])\).

Total New Old
Modular forms 5808 5808 0
Cusp forms 5712 5712 0
Eisenstein series 96 96 0

Trace form

\( 5712 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 12 q^{7} - 36 q^{8} - 24 q^{9} + O(q^{10}) \) \( 5712 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 12 q^{7} - 36 q^{8} - 24 q^{9} + 336 q^{10} - 12 q^{11} - 36 q^{12} - 24 q^{13} - 24 q^{14} - 48 q^{15} - 24 q^{16} - 24 q^{19} - 48 q^{20} - 24 q^{21} - 24 q^{22} - 24 q^{23} - 24 q^{24} - 24 q^{25} - 12 q^{26} - 36 q^{27} - 24 q^{28} - 24 q^{29} - 12 q^{30} - 24 q^{32} - 48 q^{33} - 3024 q^{34} - 24 q^{35} - 24 q^{36} + 636 q^{38} - 48 q^{39} - 2484 q^{40} - 24 q^{41} + 4056 q^{42} - 24 q^{43} + 4596 q^{44} - 12 q^{45} - 36 q^{46} - 48 q^{47} - 24 q^{48} + 12816 q^{50} + 4440 q^{51} - 2616 q^{52} - 24 q^{53} - 3276 q^{54} - 24 q^{55} - 24 q^{57} - 48 q^{58} - 24 q^{59} - 9180 q^{60} - 24 q^{61} + 72 q^{62} - 12 q^{64} - 72 q^{65} - 24 q^{66} - 24 q^{67} + 3084 q^{68} + 9468 q^{69} - 3048 q^{70} - 24 q^{71} - 24 q^{72} - 24 q^{73} - 24 q^{74} - 24 q^{76} - 48 q^{77} - 24 q^{78} - 48 q^{79} + 9456 q^{80} - 8784 q^{82} - 12 q^{83} - 36 q^{84} - 24 q^{85} - 24 q^{86} - 12 q^{87} - 36 q^{88} - 24 q^{89} - 14064 q^{90} - 24 q^{91} - 24 q^{92} + 300 q^{93} + 1656 q^{96} - 48 q^{97} + 5844 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

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