↑

Properties

Label 3200.2.cf
Level $3200$
Weight $2$
Character orbit 3200.cf
Rep. character $\chi_{3200}(107,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $4576$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.cf (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 640 \)
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 4640 3136
Cusp forms 7584 4576 3008
Eisenstein series 192 64 128

Trace form

\( 4576 q + 16 q^{2} + 16 q^{3} - 32 q^{6} + 16 q^{7} + 16 q^{8} + O(q^{10}) \) \( 4576 q + 16 q^{2} + 16 q^{3} - 32 q^{6} + 16 q^{7} + 16 q^{8} - 32 q^{11} + 16 q^{12} + 16 q^{13} - 32 q^{16} + 16 q^{17} + 16 q^{18} - 32 q^{21} + 16 q^{22} + 16 q^{23} - 32 q^{26} + 16 q^{27} + 16 q^{28} - 32 q^{31} + 16 q^{32} - 32 q^{36} + 16 q^{37} + 16 q^{38} - 32 q^{41} + 16 q^{42} + 16 q^{43} - 32 q^{46} + 16 q^{47} + 16 q^{48} - 32 q^{51} + 16 q^{52} + 16 q^{53} - 128 q^{56} + 16 q^{57} + 16 q^{58} - 256 q^{59} - 32 q^{61} + 48 q^{62} + 32 q^{63} + 352 q^{66} + 16 q^{67} + 16 q^{68} - 32 q^{71} + 16 q^{72} + 16 q^{73} + 224 q^{76} + 16 q^{77} + 16 q^{78} + 128 q^{79} - 32 q^{81} + 176 q^{82} + 16 q^{83} + 448 q^{84} - 32 q^{86} + 16 q^{87} + 16 q^{88} - 32 q^{91} - 288 q^{92} - 32 q^{93} + 256 q^{94} - 32 q^{96} + 16 q^{98} + 96 q^{99} + O(q^{100}) \)

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

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