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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

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

Display 100 coefficients 10 coefficients

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

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