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Properties

Label 387.8.y
Level $387$
Weight $8$
Character orbit 387.y
Rep. character $\chi_{387}(10,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1524$
Sturm bound $352$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 387.y (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
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 3744 1548 2196
Cusp forms 3648 1524 2124
Eisenstein series 96 24 72

Trace form

\( 1524 q + 12 q^{2} - 15828 q^{4} - 239 q^{5} - 3396 q^{7} + 5902 q^{8} + O(q^{10}) \) \( 1524 q + 12 q^{2} - 15828 q^{4} - 239 q^{5} - 3396 q^{7} + 5902 q^{8} + 1911 q^{10} + 5324 q^{11} + 11938 q^{13} + 41620 q^{14} - 883184 q^{16} + 10672 q^{17} + 45210 q^{19} + 186195 q^{20} - 70582 q^{22} + 1674 q^{23} + 2007722 q^{25} + 182293 q^{26} + 330520 q^{28} + 121019 q^{29} + 1470324 q^{31} - 263466 q^{32} + 992999 q^{34} - 1927799 q^{35} + 288343 q^{37} - 3278058 q^{38} - 2771739 q^{40} + 1485200 q^{41} + 2949704 q^{43} - 3849820 q^{44} + 4766835 q^{46} + 1380250 q^{47} - 84135732 q^{49} + 7260549 q^{50} - 6582342 q^{52} + 3502090 q^{53} - 10410138 q^{55} - 26319715 q^{56} - 1570154 q^{58} + 2165017 q^{59} + 5434962 q^{61} - 13155817 q^{62} - 64562394 q^{64} + 10859862 q^{65} - 17855096 q^{67} + 7189629 q^{68} + 14543675 q^{70} + 15741677 q^{71} + 13025705 q^{73} + 19916294 q^{74} - 53235704 q^{76} - 39954539 q^{77} - 4449205 q^{79} + 34294640 q^{80} + 16403312 q^{82} - 14405991 q^{83} + 22178136 q^{85} + 63655970 q^{86} + 42357938 q^{88} + 40322157 q^{89} + 21784821 q^{91} - 74271898 q^{92} - 71960712 q^{94} - 52010069 q^{95} + 17055413 q^{97} + 48433462 q^{98} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(387, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)