Properties

Label 450.6.v
Level $450$
Weight $6$
Character orbit 450.v
Rep. character $\chi_{450}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1200$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 450.v (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(450, [\chi])\).

Total New Old
Modular forms 3632 1200 2432
Cusp forms 3568 1200 2368
Eisenstein series 64 0 64

Trace form

\( 1200q - 2400q^{4} + 232q^{5} + 124q^{9} + O(q^{10}) \) \( 1200q - 2400q^{4} + 232q^{5} + 124q^{9} - 484q^{11} + 160q^{12} + 1568q^{14} + 340q^{15} + 38400q^{16} + 928q^{20} - 12216q^{21} + 13224q^{25} - 64896q^{26} - 25170q^{27} + 10092q^{29} + 3128q^{30} - 8868q^{31} + 49550q^{33} - 5072q^{35} + 3968q^{36} + 33308q^{39} - 26896q^{41} - 15488q^{44} + 84552q^{45} - 51050q^{47} - 5120q^{48} + 1440600q^{49} + 19376q^{50} + 44368q^{51} + 78816q^{54} + 984q^{55} - 25088q^{56} + 127458q^{59} - 7584q^{60} + 132240q^{62} + 106130q^{63} + 1228800q^{64} + 423716q^{65} + 87104q^{66} + 27570q^{67} + 104032q^{69} - 106656q^{70} + 406876q^{71} - 438080q^{74} - 699726q^{75} + 314480q^{77} - 170720q^{78} - 89508q^{79} + 29696q^{80} + 91284q^{81} + 940660q^{83} + 146592q^{84} + 40812q^{85} - 147920q^{86} - 255150q^{87} - 860068q^{89} + 116792q^{90} - 269440q^{92} - 376884q^{95} + 721892q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)