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Properties

Label 800.3.x
Level $800$
Weight $3$
Character orbit 800.x
Rep. character $\chi_{800}(51,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $596$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 800.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(800, [\chi])\).

Total New Old
Modular forms 984 620 364
Cusp forms 936 596 340
Eisenstein series 48 24 24

Trace form

\( 596 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + O(q^{10}) \) \( 596 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 12 q^{11} + 52 q^{12} + 4 q^{13} + 20 q^{14} + 8 q^{16} + 64 q^{18} + 4 q^{19} - 12 q^{21} - 72 q^{22} - 60 q^{23} + 72 q^{24} - 112 q^{26} - 92 q^{27} + 64 q^{28} + 4 q^{29} - 16 q^{32} + 8 q^{33} - 8 q^{34} + 56 q^{36} + 4 q^{37} + 116 q^{38} + 196 q^{39} - 12 q^{41} - 416 q^{42} + 100 q^{43} - 180 q^{44} - 44 q^{46} + 8 q^{47} - 48 q^{48} - 240 q^{51} + 428 q^{52} - 156 q^{53} + 24 q^{54} + 712 q^{56} + 4 q^{57} - 168 q^{58} - 124 q^{59} + 52 q^{61} + 192 q^{62} + 232 q^{64} + 564 q^{66} - 156 q^{67} + 128 q^{68} - 188 q^{69} + 244 q^{71} + 100 q^{72} + 4 q^{73} - 348 q^{74} + 500 q^{76} + 228 q^{77} - 76 q^{78} + 520 q^{79} - 636 q^{82} - 476 q^{83} - 992 q^{84} + 232 q^{86} + 452 q^{87} - 112 q^{88} + 4 q^{89} - 204 q^{91} - 768 q^{92} - 32 q^{93} - 760 q^{94} - 24 q^{96} + 8 q^{97} - 808 q^{98} - 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)