Properties

Label 29.3.f
Level $29$
Weight $3$
Character orbit 29.f
Rep. character $\chi_{29}(2,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $48$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 29.f (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(29, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 48 48 0
Eisenstein series 24 24 0

Trace form

\( 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9} + O(q^{10}) \) \( 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9} - 20 q^{10} - 8 q^{11} - 68 q^{12} - 14 q^{13} + 26 q^{14} - 4 q^{15} + 18 q^{16} - 26 q^{17} - 34 q^{18} + 2 q^{19} + 46 q^{20} + 218 q^{21} + 154 q^{22} + 56 q^{23} + 154 q^{24} - 34 q^{25} + 110 q^{26} + 126 q^{27} - 170 q^{29} + 24 q^{30} - 88 q^{31} - 132 q^{32} - 224 q^{33} - 224 q^{34} - 210 q^{35} - 434 q^{36} - 56 q^{37} - 294 q^{38} - 232 q^{39} - 492 q^{40} - 34 q^{41} - 14 q^{42} + 176 q^{43} + 126 q^{44} + 114 q^{45} + 744 q^{46} + 208 q^{47} + 640 q^{48} + 506 q^{49} + 732 q^{50} + 322 q^{51} + 690 q^{52} - 14 q^{53} - 36 q^{54} + 284 q^{55} + 332 q^{56} - 508 q^{58} - 44 q^{59} - 316 q^{60} - 30 q^{61} - 504 q^{62} - 686 q^{63} - 896 q^{64} - 554 q^{65} - 608 q^{66} - 574 q^{67} - 796 q^{68} - 806 q^{69} - 1066 q^{70} + 224 q^{71} + 748 q^{72} - 22 q^{73} + 820 q^{74} + 768 q^{75} + 514 q^{76} + 436 q^{77} + 282 q^{78} + 564 q^{79} + 1162 q^{80} + 670 q^{81} - 18 q^{82} - 126 q^{83} + 572 q^{84} + 38 q^{85} - 118 q^{87} - 384 q^{88} - 160 q^{89} - 828 q^{90} - 434 q^{91} - 1022 q^{92} - 406 q^{93} - 2 q^{94} - 642 q^{95} - 1176 q^{96} + 604 q^{97} - 102 q^{98} + 316 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(29, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
29.3.f.a 29.f 29.f $48$ $0.790$ None \(-16\) \(-12\) \(-14\) \(-10\) $\mathrm{SU}(2)[C_{28}]$