Properties

Label 1600.2.cm
Level $1600$
Weight $2$
Character orbit 1600.cm
Rep. character $\chi_{1600}(3,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $7616$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.cm (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1600 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).

Total New Old
Modular forms 7744 7744 0
Cusp forms 7616 7616 0
Eisenstein series 128 128 0

Trace form

\( 7616q - 32q^{2} - 32q^{3} - 40q^{4} - 32q^{5} - 24q^{6} - 32q^{7} - 32q^{8} - 40q^{9} + O(q^{10}) \) \( 7616q - 32q^{2} - 32q^{3} - 40q^{4} - 32q^{5} - 24q^{6} - 32q^{7} - 32q^{8} - 40q^{9} - 32q^{10} - 24q^{11} - 32q^{13} - 40q^{14} - 32q^{15} - 24q^{16} - 24q^{17} - 32q^{18} - 40q^{19} - 32q^{20} - 24q^{21} - 64q^{22} - 32q^{23} - 32q^{25} - 64q^{26} - 32q^{27} - 32q^{28} - 40q^{29} + 64q^{30} - 48q^{31} - 32q^{32} - 8q^{34} - 32q^{35} - 24q^{36} - 32q^{37} + 192q^{38} - 40q^{39} - 256q^{40} - 24q^{41} - 32q^{42} - 32q^{43} - 40q^{44} - 56q^{45} - 24q^{46} - 40q^{47} + 72q^{48} + 72q^{50} - 64q^{51} - 32q^{52} - 32q^{53} - 40q^{54} - 32q^{55} - 24q^{56} - 32q^{57} - 96q^{58} - 40q^{59} + 192q^{60} - 24q^{61} - 16q^{62} - 40q^{64} - 64q^{65} - 24q^{66} - 32q^{67} + 56q^{68} - 40q^{69} - 32q^{70} - 24q^{71} - 152q^{72} - 32q^{73} - 32q^{75} - 64q^{76} - 32q^{77} - 184q^{78} - 40q^{79} - 32q^{80} - 24q^{81} + 128q^{82} - 32q^{83} - 40q^{84} + 8q^{85} - 24q^{86} - 144q^{87} - 384q^{88} - 40q^{89} - 32q^{90} - 24q^{91} + 408q^{92} - 8q^{93} - 72q^{94} - 64q^{95} - 424q^{96} - 72q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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