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Properties

Label 387.4.g
Level $387$
Weight $4$
Character orbit 387.g
Rep. character $\chi_{387}(178,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $260$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 387.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
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 268 268 0
Cusp forms 260 260 0
Eisenstein series 8 8 0

Trace form

\( 260 q - 6 q^{2} + q^{3} - 514 q^{4} + 38 q^{5} - 21 q^{6} + 22 q^{7} + 120 q^{8} - 3 q^{9} + O(q^{10}) \) \( 260 q - 6 q^{2} + q^{3} - 514 q^{4} + 38 q^{5} - 21 q^{6} + 22 q^{7} + 120 q^{8} - 3 q^{9} + 6 q^{10} + 23 q^{11} + 12 q^{12} - 11 q^{13} - 103 q^{14} - 109 q^{15} - 2002 q^{16} + 55 q^{17} + 202 q^{18} - 77 q^{19} - 205 q^{20} - 15 q^{21} + 12 q^{22} - 2 q^{23} + 40 q^{24} + 6098 q^{25} - 306 q^{26} - 158 q^{27} - 122 q^{28} + 610 q^{29} - 1065 q^{30} - 122 q^{31} - 776 q^{32} - 469 q^{33} - 198 q^{34} + 26 q^{35} + 951 q^{36} + 166 q^{37} - 463 q^{38} + 401 q^{39} - 348 q^{40} + 425 q^{41} - 643 q^{42} + 425 q^{43} - 320 q^{44} + 379 q^{45} + 510 q^{46} - 192 q^{47} + 1274 q^{48} + 10290 q^{49} - 258 q^{50} - 1323 q^{51} + 622 q^{52} + 558 q^{53} + 2461 q^{54} + 123 q^{55} + 348 q^{56} - 465 q^{57} - 15 q^{58} - 589 q^{59} - 1615 q^{60} - 770 q^{61} - 1970 q^{62} + 1285 q^{63} + 15128 q^{64} - 2400 q^{65} - 2318 q^{66} + 400 q^{67} + 2791 q^{68} - 2501 q^{69} - 285 q^{70} - 2270 q^{71} + 3375 q^{72} - 959 q^{73} + 2778 q^{74} + 704 q^{75} + 1942 q^{76} - 1957 q^{77} + 4990 q^{78} + 418 q^{79} - 1837 q^{80} - 883 q^{81} - 1020 q^{82} + 669 q^{83} - 5281 q^{84} + 123 q^{85} + 2531 q^{86} + 1489 q^{87} + 42 q^{88} - 4010 q^{89} + 6289 q^{90} - 1558 q^{91} + 189 q^{92} + 1519 q^{93} - 1014 q^{94} + 173 q^{95} + 2736 q^{96} - 239 q^{97} - 4333 q^{98} - 1069 q^{99} + O(q^{100}) \)

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.