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Properties

Label 473.2.r
Level $473$
Weight $2$
Character orbit 473.r
Rep. character $\chi_{473}(23,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $432$
Newform subspaces $2$
Sturm bound $88$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 473 = 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 473.r (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 2 \)
Sturm bound: \(88\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 552 432 120
Cusp forms 504 432 72
Eisenstein series 48 0 48

Trace form

\( 432 q + 2 q^{3} - 68 q^{4} + 4 q^{5} - 4 q^{6} + 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 432 q + 2 q^{3} - 68 q^{4} + 4 q^{5} - 4 q^{6} + 2 q^{7} + 2 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} - 80 q^{16} - 14 q^{18} - 2 q^{19} + 8 q^{20} + 52 q^{21} - 4 q^{22} - 14 q^{23} + 16 q^{24} + 12 q^{25} + 10 q^{26} + 8 q^{27} + 12 q^{28} - 48 q^{29} - 148 q^{30} - 94 q^{31} - 100 q^{32} + 4 q^{33} - 32 q^{35} - 128 q^{36} - 22 q^{37} + 56 q^{38} + 26 q^{39} - 20 q^{40} + 12 q^{41} + 88 q^{42} - 74 q^{43} + 8 q^{44} - 20 q^{45} + 164 q^{46} + 44 q^{47} + 46 q^{48} - 190 q^{49} + 98 q^{50} - 88 q^{51} - 30 q^{52} + 46 q^{53} + 60 q^{54} + 8 q^{55} - 76 q^{56} - 112 q^{57} - 90 q^{58} - 8 q^{59} - 220 q^{60} + 10 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 12 q^{65} - 54 q^{67} + 26 q^{68} + 44 q^{69} - 40 q^{70} + 50 q^{71} + 204 q^{72} - 26 q^{73} - 98 q^{74} + 32 q^{75} + 150 q^{76} + 8 q^{77} - 28 q^{78} + 98 q^{79} + 2 q^{80} - 96 q^{81} + 48 q^{82} + 80 q^{83} + 552 q^{84} + 20 q^{85} - 130 q^{86} + 164 q^{87} - 12 q^{88} + 146 q^{90} + 62 q^{91} + 52 q^{92} - 14 q^{93} + 176 q^{94} - 22 q^{95} - 258 q^{96} - 102 q^{97} + 52 q^{98} + O(q^{100}) \)

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.r.a 473.r 43.g $216$ $3.777$ None \(-2\) \(3\) \(6\) \(-23\) $\mathrm{SU}(2)[C_{21}]$
473.2.r.b 473.r 43.g $216$ $3.777$ None \(2\) \(-1\) \(-2\) \(25\) $\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(473, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(473, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)