Properties

Label 473.2.w
Level 473
Weight 2
Character orbit w
Rep. character \(\chi_{473}(76,\cdot)\)
Character field \(\Q(\zeta_{42})\)
Dimension 504
Newforms 1
Sturm bound 88
Trace bound 0

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Defining parameters

Level: \( N \) = \( 473 = 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 473.w (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 473 \)
Character field: \(\Q(\zeta_{42})\)
Newforms: \( 1 \)
Sturm bound: \(88\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(473, [\chi])\).

Total New Old
Modular forms 552 552 0
Cusp forms 504 504 0
Eisenstein series 48 48 0

Trace form

\( 504q - 22q^{3} - 104q^{4} - 22q^{5} - 76q^{9} + O(q^{10}) \) \( 504q - 22q^{3} - 104q^{4} - 22q^{5} - 76q^{9} - 24q^{11} - 44q^{12} + 4q^{14} + 18q^{15} - 108q^{16} + 30q^{20} - 35q^{22} - 30q^{23} - 68q^{25} + 4q^{26} - 28q^{27} - 34q^{31} + 77q^{33} - 28q^{34} + 166q^{36} + 36q^{37} + 62q^{38} - 50q^{44} - 84q^{45} - 48q^{47} + 160q^{48} - 186q^{49} + 26q^{53} - 30q^{55} - 14q^{56} - 54q^{58} - 54q^{59} + 2q^{60} - 36q^{64} - 83q^{66} - 94q^{67} - 158q^{69} + 14q^{70} - 80q^{71} + 98q^{75} - 99q^{77} + 144q^{78} - 18q^{80} - 244q^{81} - 112q^{82} + 184q^{86} + 49q^{88} + 118q^{89} + 100q^{91} - 64q^{92} - 210q^{93} + 92q^{97} - 111q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(473, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
473.2.w.a \(504\) \(3.777\) None \(0\) \(-22\) \(-22\) \(0\)