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Properties

Label 387.8.bc
Level $387$
Weight $8$
Character orbit 387.bc
Rep. character $\chi_{387}(26,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1224$
Sturm bound $352$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 387.bc (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 129 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(352\)

Dimensions

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

Total New Old
Modular forms 3744 1224 2520
Cusp forms 3648 1224 2424
Eisenstein series 96 0 96

Trace form

\( 1224 q - 12800 q^{4} + 5538 q^{7} + O(q^{10}) \) \( 1224 q - 12800 q^{4} + 5538 q^{7} - 3592 q^{10} - 32382 q^{13} - 766456 q^{16} - 2184 q^{19} + 1473846 q^{25} + 912060 q^{28} - 965456 q^{31} - 432768 q^{34} - 2949846 q^{37} + 8013692 q^{40} + 2891904 q^{43} + 752812 q^{46} + 72120014 q^{49} + 23962332 q^{52} - 652224 q^{55} + 835060 q^{58} + 1690896 q^{61} - 43071488 q^{64} - 19975226 q^{67} - 19374460 q^{70} - 9211550 q^{73} - 25940992 q^{76} - 861392 q^{79} - 37086504 q^{88} + 35022898 q^{91} - 162126328 q^{94} + 16067560 q^{97} + O(q^{100}) \)

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

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