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Properties

Label 1386.4.bj
Level $1386$
Weight $4$
Character orbit 1386.bj
Rep. character $\chi_{1386}(659,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $432$
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
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 432 1312
Cusp forms 1712 432 1280
Eisenstein series 32 0 32

Trace form

\( 432 q + 4 q^{3} - 864 q^{4} - 48 q^{5} - 84 q^{9} + O(q^{10}) \) \( 432 q + 4 q^{3} - 864 q^{4} - 48 q^{5} - 84 q^{9} - 126 q^{11} + 64 q^{12} - 356 q^{15} - 3456 q^{16} + 192 q^{20} - 36 q^{22} + 5688 q^{25} + 2128 q^{27} - 72 q^{31} - 126 q^{33} + 360 q^{34} - 336 q^{36} - 288 q^{37} - 1416 q^{38} - 252 q^{45} + 1164 q^{47} - 320 q^{48} + 10584 q^{49} + 60 q^{59} + 208 q^{60} + 27648 q^{64} - 640 q^{66} - 324 q^{67} + 2188 q^{69} - 1720 q^{75} - 1536 q^{78} - 4076 q^{81} + 4176 q^{82} - 3672 q^{86} - 144 q^{88} - 2016 q^{91} - 936 q^{93} - 2268 q^{97} - 1160 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)