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Properties

Label 49.3.f
Level $49$
Weight $3$
Character orbit 49.f
Rep. character $\chi_{49}(6,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $54$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 49.f (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(49, [\chi])\).

Total New Old
Modular forms 66 66 0
Cusp forms 54 54 0
Eisenstein series 12 12 0

Trace form

\( 54 q - 5 q^{2} - 7 q^{3} - 25 q^{4} - 7 q^{5} - 35 q^{6} - 3 q^{8} + 62 q^{9} + O(q^{10}) \) \( 54 q - 5 q^{2} - 7 q^{3} - 25 q^{4} - 7 q^{5} - 35 q^{6} - 3 q^{8} + 62 q^{9} - 7 q^{10} - 38 q^{11} - 42 q^{12} - 7 q^{13} + 77 q^{14} - 89 q^{15} - 21 q^{16} + 42 q^{17} + 12 q^{18} + 49 q^{20} - 7 q^{21} + 95 q^{22} - 82 q^{23} - 133 q^{24} - 2 q^{25} - 119 q^{26} + 98 q^{27} + 238 q^{28} - 221 q^{29} - 32 q^{30} + 55 q^{32} - 7 q^{33} - 539 q^{34} + 133 q^{35} + 293 q^{36} - 124 q^{37} + 161 q^{38} + 63 q^{39} + 721 q^{40} + 91 q^{41} - 119 q^{42} - 67 q^{43} + 521 q^{44} + 77 q^{45} + 121 q^{46} + 112 q^{47} - 84 q^{49} + 164 q^{50} - 109 q^{51} - 455 q^{52} + 242 q^{53} - 322 q^{54} - 175 q^{55} - 994 q^{56} - 173 q^{57} - 171 q^{58} - 357 q^{59} - 1071 q^{60} + 77 q^{61} - 175 q^{62} + 455 q^{63} - 291 q^{64} - 7 q^{65} + 1449 q^{66} + 116 q^{67} + 161 q^{69} - 1001 q^{70} + 682 q^{71} - 402 q^{72} - 70 q^{73} + 149 q^{74} - 1267 q^{75} + 630 q^{76} + 56 q^{77} - 1323 q^{78} - 12 q^{79} + 580 q^{81} + 1428 q^{82} - 161 q^{83} + 1834 q^{84} + 443 q^{85} + 235 q^{86} + 805 q^{87} + 157 q^{88} - 161 q^{89} + 1358 q^{90} - 315 q^{91} + 950 q^{92} + 983 q^{93} - 126 q^{94} + 230 q^{95} - 238 q^{96} - 63 q^{98} + 136 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.3.f.a 49.f 49.f $54$ $1.335$ None 49.3.f.a \(-5\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$