Properties

Label 450.6.q
Level $450$
Weight $6$
Character orbit 450.q
Rep. character $\chi_{450}(31,\cdot)$
Character field $\Q(\zeta_{15})$
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.q (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 1200q + 4q^{3} + 2400q^{4} - 232q^{5} + 124q^{9} + O(q^{10}) \) \( 1200q + 4q^{3} + 2400q^{4} - 232q^{5} + 124q^{9} + 484q^{11} - 96q^{12} + 1568q^{14} + 876q^{15} + 38400q^{16} - 2136q^{17} - 2272q^{18} + 928q^{20} + 12216q^{21} + 17280q^{23} + 13224q^{25} + 64896q^{26} + 23026q^{27} + 10092q^{29} + 3688q^{30} + 8868q^{31} - 62606q^{33} + 9368q^{35} - 3968q^{36} - 40056q^{37} + 16368q^{38} + 33308q^{39} + 26896q^{41} - 67280q^{42} - 15488q^{44} - 163964q^{45} + 20066q^{47} + 3072q^{48} - 1440600q^{49} + 6288q^{50} - 44368q^{51} + 267768q^{53} + 78816q^{54} - 56160q^{55} + 25088q^{56} + 126540q^{57} + 10032q^{58} + 127458q^{59} - 92384q^{60} + 79344q^{62} - 133646q^{63} - 1228800q^{64} + 389716q^{65} - 87104q^{66} - 16542q^{67} - 68352q^{68} - 169268q^{69} + 106656q^{70} - 150476q^{71} + 72704q^{72} - 438080q^{74} - 75122q^{75} + 294272q^{77} - 240784q^{78} - 89508q^{79} - 29696q^{80} - 209084q^{81} - 276288q^{82} + 579976q^{83} + 146592q^{84} + 40812q^{85} + 147920q^{86} + 1000178q^{87} + 283132q^{89} - 355304q^{90} - 414720q^{92} - 756360q^{93} - 104272q^{95} - 228828q^{97} + 15168q^{98} + 262092q^{99} + O(q^{100}) \)

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

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