Properties

Label 450.6.s
Level $450$
Weight $6$
Character orbit 450.s
Rep. character $\chi_{450}(17,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $400$
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.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 3664 400 3264
Cusp forms 3536 400 3136
Eisenstein series 128 0 128

Trace form

\( 400q + 152q^{7} + O(q^{10}) \) \( 400q + 152q^{7} - 992q^{10} + 2892q^{13} + 25600q^{16} - 35120q^{19} + 17952q^{22} - 5104q^{25} - 9728q^{28} + 19120q^{34} - 29988q^{37} - 256q^{40} + 13440q^{43} - 46272q^{52} - 154104q^{55} + 24016q^{58} + 191856q^{67} - 397792q^{70} - 550564q^{73} - 150560q^{79} + 607248q^{82} + 640468q^{85} - 14848q^{88} + 485012q^{97} + O(q^{100}) \)

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

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