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Properties

Label 387.4.bc
Level $387$
Weight $4$
Character orbit 387.bc
Rep. character $\chi_{387}(26,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $528$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 387.bc (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 129 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(387, [\chi])\).

Total New Old
Modular forms 1632 528 1104
Cusp forms 1536 528 1008
Eisenstein series 96 0 96

Trace form

\( 528 q - 352 q^{4} - 36 q^{7} + O(q^{10}) \) \( 528 q - 352 q^{4} - 36 q^{7} - 72 q^{10} - 340 q^{13} - 1144 q^{16} - 240 q^{19} + 1196 q^{25} + 108 q^{28} - 584 q^{31} + 1152 q^{34} - 900 q^{37} + 6972 q^{40} - 128 q^{43} + 972 q^{46} + 13444 q^{49} - 3428 q^{52} - 5664 q^{55} - 1644 q^{58} - 912 q^{61} - 7552 q^{64} + 3572 q^{67} + 7140 q^{70} - 7140 q^{73} - 6528 q^{76} + 2864 q^{79} + 10584 q^{88} - 4332 q^{91} + 2520 q^{94} + 3016 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(387, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)