Properties

Label 450.2.v
Level 450
Weight 2
Character orbit v
Rep. character \(\chi_{450}(79,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 240
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.v (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{30})\)
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 752 240 512
Cusp forms 688 240 448
Eisenstein series 64 0 64

Trace form

\( 240q - 30q^{4} - 8q^{5} + 4q^{9} + O(q^{10}) \) \( 240q - 30q^{4} - 8q^{5} + 4q^{9} - 4q^{11} + 10q^{12} + 8q^{14} - 20q^{15} + 30q^{16} - 2q^{20} + 24q^{21} + 24q^{25} - 96q^{26} + 30q^{27} + 12q^{29} - 22q^{30} + 12q^{31} + 50q^{33} - 32q^{35} + 8q^{36} - 52q^{39} - 16q^{41} - 8q^{44} - 108q^{45} - 50q^{47} - 20q^{48} + 120q^{49} - 4q^{50} - 32q^{51} - 24q^{54} + 24q^{55} - 8q^{56} + 18q^{59} + 6q^{60} - 60q^{62} - 70q^{63} + 60q^{64} - 64q^{65} - 16q^{66} - 30q^{67} - 8q^{69} + 24q^{70} + 76q^{71} - 80q^{74} - 6q^{75} + 80q^{77} - 20q^{78} + 12q^{79} - 4q^{80} - 36q^{81} - 140q^{83} - 18q^{84} + 12q^{85} - 20q^{86} - 150q^{87} - 28q^{89} + 62q^{90} - 40q^{92} + 36q^{95} - 28q^{99} + O(q^{100}) \)

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.v.a \(240\) \(3.593\) None \(0\) \(0\) \(-8\) \(0\)

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