Properties

Label 1386.4.j
Level $1386$
Weight $4$
Character orbit 1386.j
Rep. character $\chi_{1386}(463,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $360$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1744 360 1384
Cusp forms 1712 360 1352
Eisenstein series 32 0 32

Trace form

\( 360 q + 8 q^{3} - 720 q^{4} + 16 q^{5} - 64 q^{9} + O(q^{10}) \) \( 360 q + 8 q^{3} - 720 q^{4} + 16 q^{5} - 64 q^{9} + 44 q^{11} + 32 q^{12} + 112 q^{14} + 92 q^{15} - 2880 q^{16} + 16 q^{18} + 64 q^{20} - 360 q^{23} - 4788 q^{25} + 296 q^{27} - 272 q^{30} - 72 q^{31} + 704 q^{33} + 512 q^{36} - 288 q^{37} + 728 q^{39} - 1024 q^{41} - 352 q^{44} - 3212 q^{45} - 1132 q^{47} - 256 q^{48} - 8820 q^{49} + 752 q^{50} + 1712 q^{51} - 1000 q^{53} + 1200 q^{54} - 1584 q^{55} + 448 q^{56} - 2248 q^{57} - 744 q^{59} - 208 q^{60} + 1248 q^{62} - 840 q^{63} + 23040 q^{64} - 1512 q^{65} + 1224 q^{67} + 4684 q^{69} + 3120 q^{71} - 128 q^{72} - 5420 q^{75} + 616 q^{77} + 1136 q^{78} - 512 q^{80} - 7112 q^{81} - 7488 q^{82} - 2368 q^{83} + 3312 q^{85} + 3040 q^{86} - 7936 q^{87} - 3280 q^{89} + 2960 q^{90} - 1440 q^{92} + 3824 q^{93} - 1864 q^{95} + 3888 q^{97} - 440 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)