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Properties

Label 1600.4.cm
Level $1600$
Weight $4$
Character orbit 1600.cm
Rep. character $\chi_{1600}(3,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $22976$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.cm (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1600 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1600, [\chi])\).

Total New Old
Modular forms 23104 23104 0
Cusp forms 22976 22976 0
Eisenstein series 128 128 0

Trace form

\( 22976 q - 32 q^{2} - 32 q^{3} - 40 q^{4} - 32 q^{5} - 24 q^{6} - 32 q^{7} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 22976 q - 32 q^{2} - 32 q^{3} - 40 q^{4} - 32 q^{5} - 24 q^{6} - 32 q^{7} - 32 q^{8} - 40 q^{9} - 32 q^{10} - 24 q^{11} - 128 q^{12} - 32 q^{13} - 40 q^{14} - 32 q^{15} - 24 q^{16} - 24 q^{17} - 32 q^{18} - 40 q^{19} - 32 q^{20} - 24 q^{21} - 896 q^{22} - 32 q^{23} - 32 q^{25} - 64 q^{26} - 32 q^{27} - 32 q^{28} - 40 q^{29} - 2288 q^{30} - 48 q^{31} - 32 q^{32} + 88 q^{34} - 32 q^{35} - 24 q^{36} - 32 q^{37} + 9600 q^{38} - 40 q^{39} - 7168 q^{40} - 24 q^{41} - 32 q^{42} - 32 q^{43} - 40 q^{44} - 248 q^{45} - 24 q^{46} - 40 q^{47} - 4920 q^{48} - 4296 q^{50} - 64 q^{51} - 32 q^{52} - 32 q^{53} - 40 q^{54} - 32 q^{55} - 24 q^{56} - 32 q^{57} - 4064 q^{58} - 40 q^{59} + 24384 q^{60} - 24 q^{61} + 32 q^{62} - 40 q^{64} - 64 q^{65} - 24 q^{66} - 32 q^{67} + 3448 q^{68} - 40 q^{69} - 32 q^{70} - 24 q^{71} + 2728 q^{72} - 32 q^{73} - 32 q^{75} - 64 q^{76} - 32 q^{77} + 11672 q^{78} - 40 q^{79} - 32 q^{80} - 24 q^{81} + 1088 q^{82} - 32 q^{83} - 40 q^{84} + 968 q^{85} - 24 q^{86} + 2544 q^{87} + 2432 q^{88} - 40 q^{89} - 32 q^{90} - 24 q^{91} + 9528 q^{92} + 184 q^{93} - 168 q^{94} - 64 q^{95} - 51624 q^{96} - 6408 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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