Properties

Label 450.6.h
Level $450$
Weight $6$
Character orbit 450.h
Rep. character $\chi_{450}(91,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $252$
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.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1832 252 1580
Cusp forms 1768 252 1516
Eisenstein series 64 0 64

Trace form

\( 252q + 4q^{2} - 1008q^{4} + 199q^{5} + 160q^{7} + 64q^{8} + O(q^{10}) \) \( 252q + 4q^{2} - 1008q^{4} + 199q^{5} + 160q^{7} + 64q^{8} - 404q^{10} - 232q^{11} + 1186q^{13} + 784q^{14} - 16128q^{16} - 1144q^{17} + 4546q^{19} - 576q^{20} - 1408q^{22} + 4350q^{23} + 21097q^{25} - 21000q^{26} + 5600q^{28} - 4128q^{29} - 1098q^{31} - 4096q^{32} - 12340q^{34} + 15894q^{35} + 12097q^{37} - 15376q^{38} - 6464q^{40} + 10700q^{41} - 31492q^{43} + 8928q^{44} + 11744q^{46} - 310q^{47} + 636868q^{49} - 10076q^{50} + 18976q^{52} - 107811q^{53} + 103718q^{55} + 12544q^{56} + 72q^{58} - 111600q^{59} - 55460q^{61} + 127472q^{62} - 258048q^{64} + 280683q^{65} + 35282q^{67} + 36576q^{68} - 27392q^{70} - 155802q^{71} - 86562q^{73} - 160424q^{74} - 9984q^{76} - 365160q^{77} + 8760q^{79} - 23296q^{80} + 272024q^{82} + 569422q^{83} + 195863q^{85} + 174808q^{86} - 3968q^{88} + 689q^{89} - 222116q^{91} - 56160q^{92} - 220512q^{94} + 253044q^{95} - 82426q^{97} + 218756q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)