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Properties

Label 387.8.f
Level $387$
Weight $8$
Character orbit 387.f
Rep. character $\chi_{387}(130,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $588$
Sturm bound $352$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 387.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 620 588 32
Cusp forms 612 588 24
Eisenstein series 8 0 8

Trace form

\( 588 q - 26 q^{3} - 18816 q^{4} - 142 q^{5} + 174 q^{6} - 5196 q^{8} - 138 q^{9} + O(q^{10}) \) \( 588 q - 26 q^{3} - 18816 q^{4} - 142 q^{5} + 174 q^{6} - 5196 q^{8} - 138 q^{9} + 16556 q^{11} - 21462 q^{12} + 50942 q^{14} + 6746 q^{15} - 1204224 q^{16} - 133052 q^{17} - 22496 q^{18} - 36352 q^{20} + 343890 q^{21} + 103174 q^{23} - 175772 q^{24} - 4665744 q^{25} - 650616 q^{26} - 966812 q^{27} + 344590 q^{29} + 1225248 q^{30} + 198654 q^{31} + 1401004 q^{32} + 522626 q^{33} + 390444 q^{34} - 2914216 q^{35} - 2873286 q^{36} - 303564 q^{37} + 827324 q^{38} + 2464286 q^{39} - 799500 q^{40} + 1888964 q^{41} - 2768650 q^{42} - 10133180 q^{44} + 261100 q^{45} + 2164488 q^{46} + 3291396 q^{47} + 9487652 q^{48} - 34588806 q^{49} + 898368 q^{50} - 4188276 q^{51} - 2243574 q^{52} - 6034224 q^{53} + 699796 q^{54} + 344604 q^{55} + 5816742 q^{56} + 2708502 q^{57} + 1897278 q^{58} + 2882366 q^{59} - 7379980 q^{60} + 1057744 q^{62} + 3119878 q^{63} + 138801780 q^{64} + 6779850 q^{65} - 10663562 q^{66} - 2940258 q^{67} + 15576130 q^{68} - 12722894 q^{69} - 4405728 q^{70} + 25386880 q^{71} + 21249180 q^{72} - 6298596 q^{74} - 8948704 q^{75} + 7301796 q^{76} - 2359666 q^{77} + 17003680 q^{78} - 9090576 q^{79} + 110742956 q^{80} + 18590558 q^{81} - 22595676 q^{82} - 4278318 q^{83} - 64078480 q^{84} + 3240996 q^{85} + 6360560 q^{86} + 3054298 q^{87} + 32723584 q^{89} - 39974792 q^{90} - 16949688 q^{91} - 30722478 q^{92} - 61484222 q^{93} - 8419338 q^{94} - 9067870 q^{95} - 30867354 q^{96} - 29228706 q^{97} + 229438580 q^{98} + 119383610 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{8}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(387, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)