Properties

Label 450.6.e
Level $450$
Weight $6$
Character orbit 450.e
Rep. character $\chi_{450}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $190$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 924 190 734
Cusp forms 876 190 686
Eisenstein series 48 0 48

Trace form

\( 190q - 4q^{2} + 13q^{3} - 1520q^{4} + 76q^{6} - 58q^{7} + 128q^{8} - 557q^{9} + O(q^{10}) \) \( 190q - 4q^{2} + 13q^{3} - 1520q^{4} + 76q^{6} - 58q^{7} + 128q^{8} - 557q^{9} + 851q^{11} - 320q^{12} + 362q^{13} + 824q^{14} - 24320q^{16} + 1746q^{17} + 296q^{18} - 1018q^{19} + 1786q^{21} - 948q^{22} + 8574q^{23} - 704q^{24} - 1424q^{26} + 16000q^{27} + 1856q^{28} + 10710q^{29} + 4976q^{31} - 1024q^{32} - 13461q^{33} - 3828q^{34} + 7792q^{36} - 9712q^{37} + 5284q^{38} + 39336q^{39} + 17999q^{41} - 30320q^{42} + 1469q^{43} - 27232q^{44} + 18960q^{46} + 6894q^{47} + 1792q^{48} - 242163q^{49} + 32833q^{51} + 5792q^{52} + 139056q^{53} - 2948q^{54} + 13184q^{56} - 71713q^{57} + 5016q^{58} - 77441q^{59} - 26176q^{61} + 53728q^{62} - 183988q^{63} + 778240q^{64} + 75560q^{66} + 14795q^{67} - 13968q^{68} - 97340q^{69} - 298104q^{71} + 12992q^{72} - 110842q^{73} + 29984q^{74} + 8144q^{76} + 89994q^{77} + 88936q^{78} - 159352q^{79} + 157543q^{81} - 193848q^{82} - 237288q^{83} - 30944q^{84} + 67052q^{86} - 222918q^{87} - 15168q^{88} - 968596q^{89} - 332072q^{91} + 137184q^{92} - 79120q^{93} + 48120q^{94} - 8192q^{96} - 212845q^{97} + 681576q^{98} + 243296q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)