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Properties

Label 473.2.n
Level $473$
Weight $2$
Character orbit 473.n
Rep. character $\chi_{473}(32,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $252$
Newform subspaces $1$
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.n (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
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 276 276 0
Cusp forms 252 252 0
Eisenstein series 24 24 0

Trace form

\( 252 q - 14 q^{3} - 46 q^{4} - 14 q^{5} + 40 q^{9} + O(q^{10}) \) \( 252 q - 14 q^{3} - 46 q^{4} - 14 q^{5} + 40 q^{9} - 6 q^{11} + 14 q^{12} - 34 q^{14} - 42 q^{15} - 6 q^{16} - 42 q^{20} + 14 q^{22} - 42 q^{23} + 20 q^{25} - 28 q^{26} - 14 q^{27} - 32 q^{31} - 14 q^{33} - 56 q^{34} - 196 q^{36} - 98 q^{38} + 98 q^{44} - 168 q^{45} + 6 q^{47} + 182 q^{48} + 168 q^{49} - 80 q^{53} + 63 q^{55} - 28 q^{56} + 60 q^{58} + 48 q^{59} + 46 q^{60} + 78 q^{64} + 11 q^{66} + 100 q^{67} + 98 q^{69} - 140 q^{70} - 28 q^{71} + 154 q^{75} - 105 q^{77} + 288 q^{78} - 2 q^{81} - 140 q^{82} + 98 q^{86} - 196 q^{88} - 28 q^{89} - 112 q^{91} - 248 q^{92} + 88 q^{97} - 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(473, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
473.2.n.a 473.n 473.n $252$ $3.777$ None \(0\) \(-14\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{14}]$