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Properties

Label 471.2.s
Level $471$
Weight $2$
Character orbit 471.s
Rep. character $\chi_{471}(2,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $1200$
Newform subspaces $1$
Sturm bound $105$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.s (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 471 \)
Character field: \(\Q(\zeta_{52})\)
Newform subspaces: \( 1 \)
Sturm bound: \(105\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(471, [\chi])\).

Total New Old
Modular forms 1296 1296 0
Cusp forms 1200 1200 0
Eisenstein series 96 96 0

Trace form

\( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9} + O(q^{10}) \) \( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9} - 52 q^{10} - 80 q^{12} - 12 q^{15} + 16 q^{16} + 12 q^{18} - 52 q^{19} - 26 q^{21} - 64 q^{22} + 18 q^{24} + 104 q^{25} - 26 q^{27} - 84 q^{28} - 34 q^{30} - 52 q^{31} - 26 q^{33} - 80 q^{34} - 26 q^{36} - 308 q^{37} + 52 q^{39} - 340 q^{40} - 26 q^{42} - 76 q^{43} - 52 q^{45} - 60 q^{46} - 130 q^{48} - 52 q^{49} - 26 q^{51} + 84 q^{52} - 246 q^{54} - 36 q^{55} - 26 q^{57} - 52 q^{58} + 14 q^{60} - 4 q^{61} - 46 q^{63} - 52 q^{64} - 22 q^{66} + 28 q^{67} - 72 q^{69} - 40 q^{70} + 46 q^{72} - 48 q^{73} - 46 q^{75} - 52 q^{76} + 146 q^{78} - 100 q^{79} + 58 q^{81} - 52 q^{82} - 156 q^{84} - 20 q^{85} + 12 q^{87} - 116 q^{88} - 26 q^{90} + 360 q^{91} - 310 q^{93} + 96 q^{94} + 176 q^{96} + 116 q^{97} - 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(471, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
471.2.s.a 471.s 471.s $1200$ $3.761$ None \(0\) \(-26\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{52}]$