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Properties

Label 3200.2.cg
Level $3200$
Weight $2$
Character orbit 3200.cg
Rep. character $\chi_{3200}(101,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $4816$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.cg (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7776 4912 2864
Cusp forms 7584 4816 2768
Eisenstein series 192 96 96

Trace form

\( 4816 q + 16 q^{2} + 16 q^{3} + 16 q^{4} - 48 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + O(q^{10}) \) \( 4816 q + 16 q^{2} + 16 q^{3} + 16 q^{4} - 48 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} - 48 q^{11} + 16 q^{12} + 16 q^{13} + 16 q^{14} - 48 q^{16} + 16 q^{17} + 16 q^{18} + 16 q^{19} - 48 q^{21} + 16 q^{22} + 16 q^{23} + 16 q^{24} - 48 q^{26} + 16 q^{27} + 16 q^{28} + 16 q^{29} - 48 q^{31} + 16 q^{32} + 16 q^{33} + 16 q^{34} - 48 q^{36} + 16 q^{37} + 16 q^{38} + 16 q^{39} - 48 q^{41} + 16 q^{42} + 16 q^{43} + 16 q^{44} - 48 q^{46} + 16 q^{47} + 16 q^{48} + 16 q^{49} - 48 q^{51} + 112 q^{52} + 16 q^{53} - 112 q^{54} + 160 q^{56} + 16 q^{57} + 160 q^{58} + 16 q^{59} - 48 q^{61} + 112 q^{62} - 176 q^{64} - 240 q^{66} + 16 q^{67} + 112 q^{68} + 16 q^{69} - 48 q^{71} + 160 q^{72} + 16 q^{73} + 224 q^{74} - 176 q^{76} + 16 q^{77} + 112 q^{78} + 16 q^{79} - 48 q^{81} + 16 q^{82} + 16 q^{83} + 16 q^{84} - 48 q^{86} + 16 q^{87} + 16 q^{88} + 16 q^{89} - 48 q^{91} + 16 q^{92} + 16 q^{93} + 16 q^{94} - 48 q^{96} + 16 q^{97} + 16 q^{98} + 16 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)