Properties

Label 387.3.o
Level $387$
Weight $3$
Character orbit 387.o
Rep. character $\chi_{387}(92,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $172$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 387.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(387, [\chi])\).

Total New Old
Modular forms 180 180 0
Cusp forms 172 172 0
Eisenstein series 8 8 0

Trace form

\( 172 q - 6 q^{2} - 5 q^{3} + 166 q^{4} - 21 q^{6} + 2 q^{7} + 3 q^{9} + O(q^{10}) \) \( 172 q - 6 q^{2} - 5 q^{3} + 166 q^{4} - 21 q^{6} + 2 q^{7} + 3 q^{9} - 6 q^{10} - 24 q^{11} + 6 q^{12} - 4 q^{13} + 69 q^{14} + 35 q^{15} - 314 q^{16} + 54 q^{17} - 20 q^{18} + 11 q^{19} + 111 q^{20} + 15 q^{21} - 30 q^{22} + 124 q^{24} - 782 q^{25} + 12 q^{26} - 32 q^{27} + 26 q^{28} - 153 q^{30} - 34 q^{31} + 23 q^{33} - 42 q^{34} + 171 q^{36} + 20 q^{37} - 267 q^{38} + 83 q^{39} + 120 q^{41} - 271 q^{42} - 29 q^{43} + 40 q^{45} - 30 q^{46} + 39 q^{47} + 278 q^{48} + 990 q^{49} + 264 q^{50} - 90 q^{51} - 10 q^{52} + 145 q^{54} - 27 q^{55} + 54 q^{57} + 9 q^{58} + 75 q^{59} + 47 q^{60} + 176 q^{61} - 444 q^{62} - 218 q^{63} - 1112 q^{64} - 438 q^{65} - 158 q^{66} - 226 q^{67} + 63 q^{68} + 265 q^{69} + 225 q^{70} + 144 q^{71} + 339 q^{72} - 82 q^{73} + 696 q^{74} + 281 q^{75} + 134 q^{76} - 3 q^{77} - 434 q^{78} + 32 q^{79} + 519 q^{80} - 265 q^{81} + 72 q^{82} - 39 q^{83} - 175 q^{84} - 27 q^{85} - 273 q^{86} - 419 q^{87} + 282 q^{88} - 432 q^{89} + 511 q^{90} - 113 q^{91} - 15 q^{92} + 268 q^{93} + 186 q^{94} + 219 q^{95} + 372 q^{96} - 73 q^{97} - 81 q^{98} + 38 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
387.3.o.a 387.o 387.o $172$ $10.545$ None \(-6\) \(-5\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$