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Properties

Label 800.6.y
Level $800$
Weight $6$
Character orbit 800.y
Rep. character $\chi_{800}(101,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1508$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.y (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(800, [\chi])\).

Total New Old
Modular forms 2424 1532 892
Cusp forms 2376 1508 868
Eisenstein series 48 24 24

Trace form

\( 1508 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + O(q^{10}) \) \( 1508 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 12 q^{11} + 1588 q^{12} + 4 q^{13} - 2476 q^{14} + 4168 q^{16} - 1616 q^{18} + 4 q^{19} - 12 q^{21} - 1208 q^{22} + 1676 q^{23} + 584 q^{24} - 12992 q^{26} - 7460 q^{27} - 2176 q^{28} + 4 q^{29} - 23088 q^{31} - 18576 q^{32} + 8 q^{33} - 5992 q^{34} + 3256 q^{36} + 4 q^{37} + 69236 q^{38} - 44900 q^{39} - 12 q^{41} - 53616 q^{42} + 32076 q^{43} + 3724 q^{44} + 63316 q^{46} - 112368 q^{48} + 19896 q^{51} + 18476 q^{52} - 49452 q^{53} - 231960 q^{54} - 16312 q^{56} + 4 q^{57} + 110568 q^{58} + 28964 q^{59} - 96172 q^{61} + 63744 q^{62} - 158752 q^{63} + 49192 q^{64} + 144996 q^{66} - 61156 q^{67} + 144064 q^{68} + 44644 q^{69} - 143852 q^{71} + 386980 q^{72} + 4 q^{73} + 326500 q^{74} - 256012 q^{76} - 14892 q^{77} - 805836 q^{78} - 435196 q^{82} - 329236 q^{83} - 597472 q^{84} + 451960 q^{86} + 282188 q^{87} + 423120 q^{88} + 4 q^{89} + 200100 q^{91} + 963520 q^{92} + 976 q^{93} - 585464 q^{94} - 712984 q^{96} + 8 q^{97} - 1206856 q^{98} - 342432 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)