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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 $480$

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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

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

Display 100 coefficients 10 coefficients

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

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