Properties

Label 450.2.w
Level 450
Weight 2
Character orbit w
Rep. character \(\chi_{450}(23,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 480
Newform subspaces 1
Sturm bound 180
Trace bound 0

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Defining parameters

Level: \( N \) = \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 450.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(450, [\chi])\).

Total New Old
Modular forms 1504 480 1024
Cusp forms 1376 480 896
Eisenstein series 128 0 128

Trace form

\( 480q - 4q^{3} + O(q^{10}) \) \( 480q - 4q^{3} + 4q^{12} + 8q^{15} - 60q^{16} + 8q^{18} + 12q^{20} + 24q^{23} - 48q^{25} + 8q^{27} + 24q^{30} - 16q^{33} + 24q^{37} - 36q^{38} + 40q^{39} - 44q^{42} + 12q^{45} - 48q^{47} - 8q^{48} - 48q^{50} + 24q^{55} + 28q^{57} - 12q^{58} - 60q^{59} - 24q^{60} + 20q^{63} + 24q^{65} + 12q^{67} - 144q^{68} - 140q^{69} + 16q^{72} - 168q^{75} - 432q^{77} - 76q^{78} + 40q^{81} + 48q^{82} - 60q^{83} - 60q^{84} + 24q^{85} - 44q^{87} - 52q^{90} + 24q^{92} - 72q^{93} - 60q^{95} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
450.2.w.a \(480\) \(3.593\) None \(0\) \(-4\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database