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Properties

Label 387.8.bb
Level $387$
Weight $8$
Character orbit 387.bb
Rep. character $\chi_{387}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $3672$
Sturm bound $352$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 387.bb (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(352\)

Dimensions

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

Total New Old
Modular forms 3720 3720 0
Cusp forms 3672 3672 0
Eisenstein series 48 48 0

Trace form

\( 3672 q + 11 q^{2} + 39 q^{3} + 19451 q^{4} + 492 q^{5} + 1274 q^{6} + 172 q^{7} - 6676 q^{8} + 16497 q^{9} + O(q^{10}) \) \( 3672 q + 11 q^{2} + 39 q^{3} + 19451 q^{4} + 492 q^{5} + 1274 q^{6} + 172 q^{7} - 6676 q^{8} + 16497 q^{9} - 154 q^{10} - 186 q^{11} - 11043 q^{12} + 3689 q^{13} - 88165 q^{14} - 4387 q^{15} + 1229051 q^{16} + 17953 q^{17} - 52284 q^{18} - 19573 q^{19} - 431697 q^{20} + 22 q^{21} - 282565 q^{22} - 8 q^{23} + 648976 q^{24} + 4656242 q^{25} + 210758 q^{26} + 245160 q^{27} - 88730 q^{28} + 196642 q^{29} - 580694 q^{30} - 1397820 q^{31} + 1829613 q^{32} - 981082 q^{33} + 709688 q^{34} - 1290299 q^{35} - 1646890 q^{36} - 12446 q^{37} + 5835543 q^{38} + 1052249 q^{39} - 94261 q^{40} - 715380 q^{41} + 672603 q^{42} - 408379 q^{43} + 3408 q^{44} - 954080 q^{45} - 602170 q^{46} + 14210 q^{47} + 6508070 q^{48} - 207174812 q^{49} + 18934710 q^{50} - 1064364 q^{51} - 3750024 q^{52} - 181486 q^{53} - 3504135 q^{54} - 78151 q^{55} + 6909073 q^{56} + 4523251 q^{57} - 517 q^{58} + 805528 q^{59} + 10712414 q^{60} + 1142243 q^{61} - 498362 q^{62} + 9730764 q^{63} - 153158164 q^{64} + 1799363 q^{65} + 16290452 q^{66} - 1419157 q^{67} + 7048845 q^{68} - 32263019 q^{69} + 12026560 q^{70} + 7481314 q^{71} - 64967464 q^{72} - 3463855 q^{73} + 28499181 q^{74} - 671413 q^{75} - 3076936 q^{76} - 14981971 q^{77} - 70467050 q^{78} + 1475635 q^{79} - 70753977 q^{80} + 59156253 q^{81} - 1895620 q^{82} - 67213601 q^{83} - 37128262 q^{84} - 78137 q^{85} + 17362510 q^{86} + 55911036 q^{87} - 57650457 q^{88} + 69732257 q^{89} + 15895918 q^{90} - 5841830 q^{91} - 47564324 q^{92} + 55522235 q^{93} + 591491 q^{94} - 27937461 q^{95} - 171338018 q^{96} - 4637131 q^{97} + 12674100 q^{98} - 68051332 q^{99} + O(q^{100}) \)

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.