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Properties

Label 1386.4.bh
Level $1386$
Weight $4$
Character orbit 1386.bh
Rep. character $\chi_{1386}(263,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1386.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1386, [\chi])\).

Total New Old
Modular forms 1744 576 1168
Cusp forms 1712 576 1136
Eisenstein series 32 0 32

Trace form

\( 576 q + 2304 q^{4} - 64 q^{9} + O(q^{10}) \) \( 576 q + 2304 q^{4} - 64 q^{9} + 24 q^{11} + 80 q^{15} + 9216 q^{16} + 504 q^{23} + 7200 q^{25} + 240 q^{26} - 24 q^{27} + 584 q^{33} - 256 q^{36} + 1536 q^{42} + 96 q^{44} + 784 q^{45} + 2184 q^{53} - 612 q^{55} + 504 q^{58} + 320 q^{60} + 36864 q^{64} + 1184 q^{66} + 560 q^{69} + 72 q^{70} + 488 q^{75} - 108 q^{77} + 960 q^{78} - 3192 q^{81} + 1200 q^{86} + 8160 q^{89} + 2016 q^{92} + 304 q^{93} + 468 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)