Properties

Label 3200.2.co
Level $3200$
Weight $2$
Character orbit 3200.co
Rep. character $\chi_{3200}(209,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1888$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.co (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 800 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7808 1952 5856
Cusp forms 7552 1888 5664
Eisenstein series 256 64 192

Trace form

\( 1888 q + 20 q^{3} - 16 q^{5} - 12 q^{9} + O(q^{10}) \) \( 1888 q + 20 q^{3} - 16 q^{5} - 12 q^{9} + 12 q^{11} - 20 q^{13} + 12 q^{19} - 12 q^{21} + 20 q^{23} - 16 q^{25} + 20 q^{27} - 12 q^{29} - 24 q^{31} - 40 q^{33} + 40 q^{35} - 20 q^{37} + 12 q^{39} - 12 q^{41} - 4 q^{45} + 8 q^{51} - 20 q^{53} + 48 q^{55} + 12 q^{59} - 12 q^{61} + 40 q^{63} - 32 q^{65} + 20 q^{67} - 12 q^{69} + 12 q^{71} - 20 q^{73} + 48 q^{75} - 20 q^{77} + 20 q^{83} + 4 q^{85} + 20 q^{87} - 12 q^{89} + 12 q^{91} + 32 q^{95} - 40 q^{97} + 56 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)