Properties

Label 450.6.j
Level $450$
Weight $6$
Character orbit 450.j
Rep. character $\chi_{450}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $180$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 924 180 744
Cusp forms 876 180 696
Eisenstein series 48 0 48

Trace form

\( 180q + 1440q^{4} + 160q^{6} + 1384q^{9} + O(q^{10}) \) \( 180q + 1440q^{4} + 160q^{6} + 1384q^{9} + 276q^{11} + 1488q^{14} - 23040q^{16} - 11336q^{21} + 1280q^{24} + 16224q^{26} + 432q^{29} - 8868q^{31} + 23168q^{36} - 10312q^{39} - 56196q^{41} + 8832q^{44} + 37920q^{46} + 219750q^{49} + 165948q^{51} + 43976q^{54} - 23808q^{56} + 131658q^{59} + 46740q^{61} - 737280q^{64} + 169704q^{66} - 6648q^{69} - 392304q^{71} + 90000q^{74} + 54612q^{79} - 334216q^{81} - 166528q^{84} + 28200q^{86} + 133392q^{89} - 129360q^{91} - 96240q^{94} - 20480q^{96} + 1342482q^{99} + O(q^{100}) \)

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

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