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Properties

Label 3200.2.df
Level $3200$
Weight $2$
Character orbit 3200.df
Rep. character $\chi_{3200}(29,\cdot)$
Character field $\Q(\zeta_{160})$
Dimension $30592$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.df (of order \(160\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3200 \)
Character field: \(\Q(\zeta_{160})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3200, [\chi])\).

Total New Old
Modular forms 30848 30848 0
Cusp forms 30592 30592 0
Eisenstein series 256 256 0

Trace form

\( 30592 q - 80 q^{2} - 80 q^{3} - 48 q^{4} - 64 q^{5} - 48 q^{6} - 80 q^{8} - 48 q^{9} + O(q^{10}) \) \( 30592 q - 80 q^{2} - 80 q^{3} - 48 q^{4} - 64 q^{5} - 48 q^{6} - 80 q^{8} - 48 q^{9} - 64 q^{10} - 48 q^{11} - 80 q^{12} - 80 q^{13} - 48 q^{14} - 64 q^{15} - 48 q^{16} - 80 q^{17} - 48 q^{19} - 64 q^{20} - 48 q^{21} - 80 q^{22} - 80 q^{23} - 128 q^{24} - 64 q^{25} - 128 q^{26} - 80 q^{27} - 80 q^{28} - 48 q^{29} - 64 q^{30} - 48 q^{31} - 80 q^{33} - 48 q^{34} - 64 q^{35} - 48 q^{36} - 80 q^{37} - 80 q^{38} - 48 q^{39} - 64 q^{40} - 48 q^{41} - 80 q^{42} - 48 q^{44} - 64 q^{45} - 48 q^{46} - 80 q^{47} - 80 q^{48} - 128 q^{49} - 16 q^{50} - 128 q^{51} - 80 q^{52} - 80 q^{53} - 48 q^{54} - 64 q^{55} - 48 q^{56} - 80 q^{58} - 48 q^{59} + 128 q^{60} - 48 q^{61} - 80 q^{62} - 48 q^{64} - 48 q^{66} - 80 q^{67} - 48 q^{69} + 128 q^{70} - 48 q^{71} - 80 q^{72} - 80 q^{73} - 128 q^{74} - 64 q^{75} - 128 q^{76} - 80 q^{77} - 80 q^{78} - 48 q^{79} - 16 q^{80} - 48 q^{81} - 80 q^{83} - 48 q^{84} - 64 q^{85} - 48 q^{86} - 80 q^{87} - 80 q^{88} - 48 q^{89} - 64 q^{90} - 48 q^{91} - 80 q^{92} - 48 q^{94} - 64 q^{95} - 48 q^{96} - 80 q^{97} - 80 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces

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