Properties

Label 1600.2.cq
Level $1600$
Weight $2$
Character orbit 1600.cq
Rep. character $\chi_{1600}(29,\cdot)$
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.cq (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

\( 7616q - 40q^{2} - 40q^{3} - 24q^{4} - 32q^{5} - 24q^{6} - 40q^{8} - 24q^{9} + O(q^{10}) \) \( 7616q - 40q^{2} - 40q^{3} - 24q^{4} - 32q^{5} - 24q^{6} - 40q^{8} - 24q^{9} - 32q^{10} - 24q^{11} - 40q^{12} - 40q^{13} - 24q^{14} - 32q^{15} - 24q^{16} - 40q^{17} - 24q^{19} - 32q^{20} - 24q^{21} - 40q^{22} - 40q^{23} - 64q^{24} - 32q^{25} + 16q^{26} - 40q^{27} - 40q^{28} - 24q^{29} - 112q^{30} - 24q^{34} - 32q^{35} - 264q^{36} - 40q^{37} - 40q^{38} - 24q^{39} + 128q^{40} - 24q^{41} - 40q^{42} - 24q^{44} - 32q^{45} - 24q^{46} - 40q^{47} - 40q^{48} - 64q^{49} - 56q^{50} - 64q^{51} - 40q^{52} - 40q^{53} - 24q^{54} + 32q^{55} - 24q^{56} - 40q^{58} - 24q^{59} - 128q^{60} - 24q^{61} - 40q^{62} - 80q^{63} - 24q^{64} - 64q^{65} + 8q^{66} - 40q^{67} - 24q^{69} - 128q^{70} - 24q^{71} - 40q^{72} - 40q^{73} - 64q^{74} + 32q^{75} - 64q^{76} - 40q^{77} - 40q^{78} - 24q^{79} - 56q^{80} - 24q^{81} - 40q^{83} - 24q^{84} - 32q^{85} - 24q^{86} - 40q^{87} - 40q^{88} - 24q^{89} - 32q^{90} - 24q^{91} - 40q^{92} + 56q^{94} - 24q^{96} - 40q^{98} - 16q^{99} + O(q^{100}) \)

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

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