Properties

Label 473.2.f
Level $473$
Weight $2$
Character orbit 473.f
Rep. character $\chi_{473}(130,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $168$
Newform subspaces $2$
Sturm bound $88$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 473 = 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 473.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(88\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 184 168 16
Cusp forms 168 168 0
Eisenstein series 16 0 16

Trace form

\( 168 q - 2 q^{3} - 42 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{7} - 32 q^{9} + O(q^{10}) \) \( 168 q - 2 q^{3} - 42 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{7} - 32 q^{9} + 8 q^{10} - 4 q^{11} + 32 q^{12} - q^{13} + 4 q^{14} + 14 q^{15} - 42 q^{16} + 2 q^{17} - 16 q^{18} - 8 q^{19} + 22 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 8 q^{24} - 48 q^{25} + 14 q^{26} - 8 q^{27} + 12 q^{28} + 22 q^{29} - 48 q^{30} + 4 q^{31} - 40 q^{32} - 32 q^{33} - 44 q^{34} - 36 q^{35} - 54 q^{36} - 34 q^{37} + 2 q^{38} + 58 q^{39} + 4 q^{40} + 24 q^{41} + 26 q^{42} + 16 q^{43} - 80 q^{44} + 80 q^{45} - 56 q^{46} + 6 q^{47} - 6 q^{48} - 58 q^{49} - 52 q^{50} + 52 q^{51} - 46 q^{52} - 26 q^{53} + 120 q^{54} - 2 q^{55} + 4 q^{56} + 36 q^{57} + 56 q^{58} - 22 q^{59} - 126 q^{60} + 8 q^{61} + 18 q^{62} - 14 q^{63} - 18 q^{64} - 52 q^{66} + 70 q^{67} - 40 q^{68} - 106 q^{69} - 48 q^{70} - 30 q^{71} + 118 q^{72} + 78 q^{73} - 44 q^{75} + 36 q^{76} + 66 q^{77} + 112 q^{78} - 82 q^{79} - 6 q^{80} + 2 q^{81} - 32 q^{82} + 18 q^{83} - 72 q^{84} + 40 q^{85} + 8 q^{87} - 80 q^{88} + 20 q^{89} - 80 q^{90} + 54 q^{91} - 10 q^{92} + 4 q^{93} - 20 q^{95} - 46 q^{96} - 75 q^{97} + 60 q^{98} - 39 q^{99} + O(q^{100}) \)

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.f.a 473.f 11.c $76$ $3.777$ None \(0\) \(5\) \(13\) \(-4\) $\mathrm{SU}(2)[C_{5}]$
473.2.f.b 473.f 11.c $92$ $3.777$ None \(0\) \(-7\) \(-15\) \(-4\) $\mathrm{SU}(2)[C_{5}]$