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Properties

Label 387.4.f
Level $387$
Weight $4$
Character orbit 387.f
Rep. character $\chi_{387}(130,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $252$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 387.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(387, [\chi])\).

Total New Old
Modular forms 268 252 16
Cusp forms 260 252 8
Eisenstein series 8 0 8

Trace form

\( 252 q + 4 q^{3} - 504 q^{4} + 8 q^{5} + 30 q^{6} - 12 q^{8} - 96 q^{9} + O(q^{10}) \) \( 252 q + 4 q^{3} - 504 q^{4} + 8 q^{5} + 30 q^{6} - 12 q^{8} - 96 q^{9} + 80 q^{11} + 330 q^{12} + 62 q^{14} - 4 q^{15} - 2016 q^{16} - 176 q^{17} - 128 q^{18} + 128 q^{20} - 24 q^{21} + 64 q^{23} + 388 q^{24} - 3294 q^{25} + 1704 q^{26} + 292 q^{27} - 536 q^{29} - 432 q^{30} - 36 q^{31} - 932 q^{32} + 344 q^{33} + 396 q^{34} - 16 q^{35} - 582 q^{36} - 144 q^{37} - 124 q^{38} - 1492 q^{39} + 180 q^{40} + 176 q^{41} + 1454 q^{42} + 2404 q^{44} + 580 q^{45} + 72 q^{46} + 1176 q^{47} - 604 q^{48} - 6174 q^{49} + 528 q^{50} + 1260 q^{51} - 918 q^{52} - 1344 q^{53} - 2756 q^{54} - 2016 q^{55} - 714 q^{56} + 624 q^{57} - 90 q^{58} + 2768 q^{59} - 1180 q^{60} + 3520 q^{62} - 1268 q^{63} + 18036 q^{64} - 840 q^{65} + 1510 q^{66} + 612 q^{67} + 2434 q^{68} - 2984 q^{69} + 72 q^{70} - 2624 q^{71} + 204 q^{72} + 2124 q^{74} + 356 q^{75} - 1116 q^{76} - 112 q^{77} + 3664 q^{78} - 1188 q^{79} - 1684 q^{80} + 2072 q^{81} - 5148 q^{82} + 3180 q^{83} + 2288 q^{84} + 936 q^{85} + 860 q^{86} + 364 q^{87} - 1640 q^{89} - 8132 q^{90} + 1008 q^{91} - 2094 q^{92} + 5200 q^{93} + 1350 q^{94} + 410 q^{95} - 8970 q^{96} + 1944 q^{97} - 940 q^{98} + 2660 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(387, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)