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Properties

Label 473.2.q
Level $473$
Weight $2$
Character orbit 473.q
Rep. character $\chi_{473}(36,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $336$
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.q (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{15})\)
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 368 368 0
Cusp forms 336 336 0
Eisenstein series 32 32 0

Trace form

\( 336 q - 12 q^{2} - 7 q^{3} - 96 q^{4} - 7 q^{5} + 7 q^{6} - 10 q^{7} + 36 q^{8} + 23 q^{9} + O(q^{10}) \) \( 336 q - 12 q^{2} - 7 q^{3} - 96 q^{4} - 7 q^{5} + 7 q^{6} - 10 q^{7} + 36 q^{8} + 23 q^{9} + 4 q^{10} - 20 q^{11} - 2 q^{12} - 8 q^{13} + 2 q^{14} - 11 q^{15} - 60 q^{16} - 2 q^{17} - 26 q^{18} - 16 q^{19} - 13 q^{20} - 44 q^{21} - 34 q^{22} + 18 q^{23} + 23 q^{24} + 21 q^{25} - 11 q^{26} - 52 q^{27} - 6 q^{28} - 7 q^{29} - 39 q^{30} - q^{31} - 80 q^{32} + 44 q^{33} - 22 q^{34} + 18 q^{35} + 111 q^{36} + 7 q^{37} + 13 q^{38} + 32 q^{39} - 22 q^{40} - 36 q^{41} - 80 q^{42} - 10 q^{43} + 128 q^{44} - 68 q^{45} - 70 q^{46} - 48 q^{47} - 45 q^{48} + 16 q^{49} - 2 q^{50} + 2 q^{51} + 37 q^{52} - 10 q^{53} + 60 q^{54} + 23 q^{55} - 82 q^{56} - 14 q^{58} + 28 q^{59} + 81 q^{60} - 14 q^{61} + 21 q^{62} - 7 q^{63} + 12 q^{64} - 168 q^{65} - 35 q^{66} - 16 q^{67} + 43 q^{68} + 91 q^{69} - 30 q^{70} - 15 q^{71} + 95 q^{72} - 15 q^{73} + 63 q^{74} - 244 q^{75} + 78 q^{76} + 18 q^{77} - 172 q^{78} - 53 q^{79} + 87 q^{80} + 79 q^{81} - 58 q^{82} - 3 q^{83} - 126 q^{84} - 34 q^{85} - 69 q^{86} - 32 q^{87} + 218 q^{88} + 82 q^{89} + 26 q^{90} - 39 q^{91} - 41 q^{92} - 64 q^{93} + 294 q^{94} - 43 q^{95} + 88 q^{96} - 96 q^{97} + 24 q^{98} + 165 q^{99} + O(q^{100}) \)

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.q.a 473.q 473.q $336$ $3.777$ None \(-12\) \(-7\) \(-7\) \(-10\) $\mathrm{SU}(2)[C_{15}]$