Properties

Label 387.8.l
Level $387$
Weight $8$
Character orbit 387.l
Rep. character $\chi_{387}(128,\cdot)$
Character field $\Q(\zeta_{6})$
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.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 612 q - 19458 q^{4} + 2796 q^{6} + 1842 q^{9} + O(q^{10}) \) \( 612 q - 19458 q^{4} + 2796 q^{6} + 1842 q^{9} + 504 q^{10} - 1092 q^{11} + 3692 q^{13} - 53670 q^{14} + 4370 q^{15} - 1229058 q^{16} + 23518 q^{21} - 6 q^{23} + 163006 q^{24} - 4656252 q^{25} - 215050 q^{31} + 95576 q^{36} + 3502218 q^{38} - 188508 q^{40} - 1590096 q^{41} - 408374 q^{43} - 85296 q^{47} + 34230786 q^{49} + 1010942 q^{52} - 7154878 q^{54} + 6548358 q^{56} - 5083038 q^{57} + 510 q^{58} - 10072962 q^{59} + 4784812 q^{60} + 153158136 q^{64} + 11067858 q^{66} - 4672858 q^{67} + 9066816 q^{68} - 9944676 q^{74} + 38963428 q^{78} - 2951260 q^{79} - 54208822 q^{81} - 5584014 q^{83} + 10328768 q^{84} + 38393193 q^{86} - 31712682 q^{87} - 39183296 q^{90} + 762 q^{92} + 28505166 q^{95} + 12971314 q^{96} + 22503918 q^{97} + 27546178 q^{99} + O(q^{100}) \)

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

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