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Properties

Label 387.8.e
Level $387$
Weight $8$
Character orbit 387.e
Rep. character $\chi_{387}(49,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $612$
Sturm bound $352$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 387.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(352\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(387, [\chi])\).

Total New Old
Modular forms 620 620 0
Cusp forms 612 612 0
Eisenstein series 8 8 0

Trace form

\( 612 q - 18 q^{2} - 53 q^{3} - 19458 q^{4} - 499 q^{5} - 1281 q^{6} - 165 q^{7} + 6648 q^{8} - 5955 q^{9} + O(q^{10}) \) \( 612 q - 18 q^{2} - 53 q^{3} - 19458 q^{4} - 499 q^{5} - 1281 q^{6} - 165 q^{7} + 6648 q^{8} - 5955 q^{9} + 126 q^{10} + 179 q^{11} + 9237 q^{12} - 3696 q^{13} - 35266 q^{14} + 4373 q^{15} - 1229058 q^{16} - 17981 q^{17} + 52270 q^{18} + 12216 q^{19} + 431690 q^{20} + 15273 q^{21} + 35766 q^{22} + q^{23} + 390370 q^{24} - 4656249 q^{25} - 210786 q^{26} - 245174 q^{27} - 25986 q^{28} - 196649 q^{29} - 394875 q^{30} - 107523 q^{31} - 388040 q^{32} + 297791 q^{33} - 88599 q^{34} + 743396 q^{35} + 1646883 q^{36} + 12432 q^{37} - 1009918 q^{38} - 1052263 q^{39} + 94254 q^{40} + 715373 q^{41} - 2632183 q^{42} + 408372 q^{43} - 3464 q^{44} - 2818136 q^{45} + 602142 q^{46} - 14217 q^{47} - 4548532 q^{48} - 34946823 q^{49} + 5565276 q^{50} + 1274679 q^{51} + 440193 q^{52} + 181458 q^{53} + 3504121 q^{54} + 78123 q^{55} + 4620522 q^{56} - 4523265 q^{57} + 510 q^{58} + 614450 q^{59} - 8752876 q^{60} - 1142250 q^{61} + 498334 q^{62} + 1775878 q^{63} + 153158136 q^{64} - 1799370 q^{65} + 865246 q^{66} + 1419150 q^{67} - 23710406 q^{68} - 4948295 q^{69} - 496965 q^{70} - 7481342 q^{71} - 10545078 q^{72} + 3463827 q^{73} - 28500084 q^{74} - 10434661 q^{75} + 3076929 q^{76} + 26511566 q^{77} - 17736758 q^{78} - 1475628 q^{79} - 29598037 q^{80} + 15335297 q^{81} + 1895592 q^{82} - 24279570 q^{83} - 24545665 q^{84} + 78123 q^{85} + 33133355 q^{86} + 33286261 q^{87} + 10265490 q^{88} - 29513120 q^{89} + 5477749 q^{90} + 77001 q^{91} + 47564310 q^{92} + 42406414 q^{93} - 591498 q^{94} + 27937454 q^{95} - 98267346 q^{96} + 4637124 q^{97} - 18439825 q^{98} - 28624597 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

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