Properties

Label 731.2.u
Level $731$
Weight $2$
Character orbit 731.u
Rep. character $\chi_{731}(52,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $696$
Newform subspaces $2$
Sturm bound $132$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.u (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

Total New Old
Modular forms 816 696 120
Cusp forms 768 696 72
Eisenstein series 48 0 48

Trace form

\( 696 q + 4 q^{2} + 2 q^{3} - 108 q^{4} + 4 q^{5} - 4 q^{6} - 22 q^{7} - 28 q^{8} + 24 q^{9} + O(q^{10}) \) \( 696 q + 4 q^{2} + 2 q^{3} - 108 q^{4} + 4 q^{5} - 4 q^{6} - 22 q^{7} - 28 q^{8} + 24 q^{9} - 8 q^{10} - 16 q^{11} - 4 q^{12} - 18 q^{13} - 22 q^{14} - 16 q^{15} - 60 q^{16} - 24 q^{18} - 4 q^{19} + 40 q^{20} + 52 q^{21} + 32 q^{22} - 28 q^{23} + 16 q^{24} + 32 q^{25} - 20 q^{26} - 16 q^{27} + 10 q^{28} - 40 q^{29} - 76 q^{30} - 104 q^{31} + 10 q^{32} + 34 q^{33} + 4 q^{34} + 44 q^{35} - 290 q^{36} - 14 q^{37} - 58 q^{38} - 62 q^{39} + 204 q^{40} + 36 q^{41} - 66 q^{43} - 196 q^{44} - 40 q^{45} + 4 q^{46} + 44 q^{47} + 202 q^{48} - 314 q^{49} + 58 q^{50} - 16 q^{51} - 22 q^{52} + 20 q^{53} - 24 q^{54} - 100 q^{55} + 114 q^{56} - 112 q^{57} - 56 q^{58} - 46 q^{59} - 164 q^{60} + 22 q^{61} - 86 q^{62} - 34 q^{63} - 224 q^{64} - 136 q^{65} - 52 q^{66} - 50 q^{67} - 22 q^{69} - 152 q^{70} + 32 q^{71} + 102 q^{72} + 56 q^{73} + 154 q^{74} - 86 q^{75} - 56 q^{76} + 154 q^{77} + 96 q^{78} + 14 q^{79} + 20 q^{80} - 194 q^{81} - 64 q^{82} + 106 q^{83} + 440 q^{84} + 52 q^{85} + 144 q^{86} - 156 q^{87} + 280 q^{88} - 70 q^{89} + 386 q^{90} + 150 q^{91} + 24 q^{92} + 40 q^{94} - 194 q^{95} - 156 q^{96} + 98 q^{97} - 84 q^{98} + 34 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
731.2.u.a 731.u 43.g $348$ $5.837$ None \(-2\) \(5\) \(3\) \(-71\) $\mathrm{SU}(2)[C_{21}]$
731.2.u.b 731.u 43.g $348$ $5.837$ None \(6\) \(-3\) \(1\) \(49\) $\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(731, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(731, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)