Properties

Label 1600.2.bn
Level $1600$
Weight $2$
Character orbit 1600.bn
Rep. character $\chi_{1600}(149,\cdot)$
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.bn (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

\( 1136q + 16q^{4} - 16q^{6} + 16q^{9} + O(q^{10}) \) \( 1136q + 16q^{4} - 16q^{6} + 16q^{9} - 16q^{11} + 16q^{14} - 16q^{16} + 16q^{19} - 16q^{21} + 16q^{24} + 64q^{26} + 16q^{29} + 16q^{34} + 144q^{36} + 16q^{39} - 16q^{41} + 16q^{44} - 16q^{46} + 16q^{49} - 80q^{51} - 112q^{54} - 64q^{56} + 144q^{59} - 16q^{61} - 176q^{64} + 208q^{66} + 16q^{69} - 144q^{71} + 64q^{74} + 112q^{76} + 80q^{79} - 16q^{81} + 240q^{84} - 16q^{86} + 16q^{89} - 16q^{91} - 112q^{94} - 16q^{96} - 32q^{99} + O(q^{100}) \)

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

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