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Properties

Label 800.4.ba
Level $800$
Weight $4$
Character orbit 800.ba
Rep. character $\chi_{800}(149,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $856$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 800.ba (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(800, [\chi])\).

Total New Old
Modular forms 1464 872 592
Cusp forms 1416 856 560
Eisenstein series 48 16 32

Trace form

\( 856 q + 8 q^{4} - 8 q^{6} + 8 q^{9} + O(q^{10}) \) \( 856 q + 8 q^{4} - 8 q^{6} + 8 q^{9} - 8 q^{11} - 408 q^{14} - 8 q^{16} + 8 q^{19} - 8 q^{21} + 920 q^{24} + 32 q^{26} + 8 q^{29} - 1504 q^{31} - 56 q^{34} + 872 q^{36} + 8 q^{39} - 8 q^{41} + 8 q^{44} - 8 q^{46} + 3184 q^{51} - 1720 q^{54} + 160 q^{56} + 2760 q^{59} + 3640 q^{61} + 2192 q^{64} - 12136 q^{66} - 2104 q^{69} - 456 q^{71} + 5448 q^{74} + 10232 q^{76} + 4832 q^{84} + 2360 q^{86} + 8 q^{89} - 8 q^{91} - 13344 q^{94} - 2040 q^{96} - 10400 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)