↑

Properties

Label 1600.4.bn
Level $1600$
Weight $4$
Character orbit 1600.bn
Rep. character $\chi_{1600}(149,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $3440$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.bn (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1600, [\chi])\).

Total New Old
Modular forms 5808 3472 2336
Cusp forms 5712 3440 2272
Eisenstein series 96 32 64

Trace form

\( 3440 q + 16 q^{4} - 16 q^{6} + 16 q^{9} + O(q^{10}) \) \( 3440 q + 16 q^{4} - 16 q^{6} + 16 q^{9} - 16 q^{11} + 16 q^{14} - 16 q^{16} + 16 q^{19} - 16 q^{21} + 16 q^{24} - 96 q^{26} + 16 q^{29} + 16 q^{34} - 1776 q^{36} + 16 q^{39} - 16 q^{41} + 16 q^{44} - 16 q^{46} + 16 q^{49} - 5968 q^{51} - 3440 q^{54} + 320 q^{56} - 5488 q^{59} - 16 q^{61} + 12112 q^{64} - 10832 q^{66} + 16 q^{69} + 880 q^{71} + 2272 q^{74} + 11888 q^{76} + 11344 q^{79} - 16 q^{81} + 8304 q^{84} - 16 q^{86} + 16 q^{89} - 16 q^{91} + 11920 q^{94} - 16 q^{96} - 416 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)