Properties

Label 450.6.p
Level $450$
Weight $6$
Character orbit 450.p
Rep. character $\chi_{450}(257,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $360$
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.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1848 360 1488
Cusp forms 1752 360 1392
Eisenstein series 96 0 96

Trace form

\( 360q - 4q^{3} - 320q^{6} + O(q^{10}) \) \( 360q - 4q^{3} - 320q^{6} - 4560q^{11} + 64q^{12} + 46080q^{16} - 2272q^{18} - 1520q^{21} - 15816q^{23} + 12248q^{27} - 52696q^{33} + 10240q^{36} - 40056q^{37} + 49104q^{38} + 50040q^{41} - 14384q^{42} + 75840q^{46} - 29568q^{47} - 2048q^{48} - 22840q^{51} + 7680q^{56} + 62948q^{57} - 10032q^{58} - 93480q^{61} + 98240q^{63} - 63920q^{66} - 11028q^{67} - 51264q^{68} - 72704q^{72} + 694128q^{77} + 255744q^{78} + 1211840q^{81} + 276288q^{82} + 46740q^{83} + 324720q^{86} - 413704q^{87} + 258720q^{91} - 253056q^{92} - 715252q^{93} - 40960q^{96} - 16884q^{97} + O(q^{100}) \)

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

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