Properties

Label 1600.2.bl
Level $1600$
Weight $2$
Character orbit 1600.bl
Rep. character $\chi_{1600}(43,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1136$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.bl (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1968 1168 800
Cusp forms 1872 1136 736
Eisenstein series 96 32 64

Trace form

\( 1136q + 8q^{2} + 8q^{3} - 16q^{6} + 8q^{7} + 8q^{8} + O(q^{10}) \) \( 1136q + 8q^{2} + 8q^{3} - 16q^{6} + 8q^{7} + 8q^{8} - 16q^{11} - 24q^{12} + 8q^{13} - 64q^{14} - 16q^{16} + 8q^{18} - 16q^{21} + 40q^{22} + 8q^{23} + 32q^{24} - 16q^{26} + 8q^{27} + 8q^{28} - 32q^{31} + 8q^{32} + 32q^{34} - 16q^{36} + 8q^{37} + 64q^{38} - 16q^{41} + 8q^{42} + 8q^{43} - 16q^{46} + 16q^{47} - 96q^{48} + 48q^{51} + 8q^{52} + 8q^{53} + 32q^{56} + 8q^{57} + 72q^{58} - 16q^{61} + 24q^{62} - 208q^{66} + 8q^{67} - 80q^{68} + 128q^{69} + 112q^{71} + 128q^{72} + 8q^{73} - 144q^{76} + 8q^{77} + 160q^{78} - 64q^{79} - 16q^{81} + 8q^{82} + 8q^{83} - 16q^{86} + 120q^{87} - 80q^{88} - 16q^{91} + 232q^{92} + 32q^{93} - 32q^{94} - 16q^{96} + 48q^{98} + 256q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)