Properties

Label 450.6.w
Level $450$
Weight $6$
Character orbit 450.w
Rep. character $\chi_{450}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2400$
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.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 7264 2400 4864
Cusp forms 7136 2400 4736
Eisenstein series 128 0 128

Trace form

\( 2400q - 4q^{3} + O(q^{10}) \) \( 2400q - 4q^{3} + 64q^{12} + 3128q^{15} - 76800q^{16} - 2272q^{18} - 5568q^{20} - 15816q^{23} - 26448q^{25} + 12248q^{27} - 6816q^{30} - 52696q^{33} - 40056q^{37} + 49104q^{38} - 7160q^{39} - 14384q^{42} - 71868q^{45} - 29568q^{47} - 2048q^{48} + 76992q^{50} - 55176q^{55} - 224972q^{57} - 10032q^{58} - 856860q^{59} - 115584q^{60} + 737780q^{63} - 35976q^{65} - 11028q^{67} + 205056q^{68} - 29540q^{69} - 72704q^{72} - 496488q^{75} - 1192752q^{77} - 3856q^{78} - 117800q^{81} + 276288q^{82} + 46740q^{83} + 488640q^{84} + 81624q^{85} + 384196q^{87} - 399952q^{90} - 253056q^{92} - 1480272q^{93} - 3660q^{95} - 16884q^{97} + O(q^{100}) \)

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

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