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Properties

Label 473.2.e
Level $473$
Weight $2$
Character orbit 473.e
Rep. character $\chi_{473}(122,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $72$
Newform subspaces $4$
Sturm bound $88$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 473 = 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 473.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(88\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

Total New Old
Modular forms 92 72 20
Cusp forms 84 72 12
Eisenstein series 8 0 8

Trace form

\( 72 q - 2 q^{3} + 68 q^{4} - 4 q^{5} + 4 q^{6} - 2 q^{7} - 30 q^{9} + O(q^{10}) \) \( 72 q - 2 q^{3} + 68 q^{4} - 4 q^{5} + 4 q^{6} - 2 q^{7} - 30 q^{9} - 4 q^{12} + 8 q^{13} - 4 q^{14} + 52 q^{16} + 14 q^{18} + 2 q^{19} - 36 q^{20} - 52 q^{21} + 4 q^{22} - 16 q^{24} - 40 q^{25} - 24 q^{26} - 8 q^{27} - 12 q^{28} + 20 q^{29} + 8 q^{30} - 4 q^{31} - 40 q^{32} - 4 q^{33} + 88 q^{35} - 54 q^{36} - 6 q^{37} + 28 q^{38} - 12 q^{39} + 20 q^{40} + 16 q^{41} + 24 q^{42} + 18 q^{43} - 8 q^{44} - 36 q^{45} - 52 q^{46} - 16 q^{47} - 46 q^{48} - 34 q^{49} - 42 q^{50} + 32 q^{51} + 58 q^{52} + 10 q^{53} - 60 q^{54} - 8 q^{55} - 22 q^{56} - 14 q^{57} - 8 q^{58} + 8 q^{59} + 80 q^{60} - 24 q^{61} + 24 q^{62} - 4 q^{63} + 4 q^{64} - 12 q^{65} - 2 q^{67} - 26 q^{68} + 12 q^{69} - 44 q^{70} - 36 q^{71} + 76 q^{72} + 26 q^{73} - 42 q^{74} - 88 q^{75} + 46 q^{76} - 8 q^{77} - 28 q^{78} - 42 q^{79} - 86 q^{80} + 12 q^{81} + 8 q^{82} + 32 q^{83} - 48 q^{84} - 20 q^{85} - 38 q^{86} + 116 q^{87} + 12 q^{88} - 28 q^{89} + 260 q^{90} - 6 q^{91} + 18 q^{92} + 14 q^{93} - 8 q^{94} + 22 q^{95} + 62 q^{96} + 60 q^{97} + 88 q^{98} + O(q^{100}) \)

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.e.a 473.e 43.c $2$ $3.777$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
473.2.e.b 473.e 43.c $2$ $3.777$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-\zeta_{6})q^{3}-q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
473.2.e.c 473.e 43.c $34$ $3.777$ None \(-4\) \(0\) \(5\) \(2\) $\mathrm{SU}(2)[C_{3}]$
473.2.e.d 473.e 43.c $34$ $3.777$ None \(0\) \(-2\) \(-7\) \(-8\) $\mathrm{SU}(2)[C_{3}]$

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

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