Properties

Label 1386.4.by
Level $1386$
Weight $4$
Character orbit 1386.by
Rep. character $\chi_{1386}(169,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1728$
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.by (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 6976 1728 5248
Cusp forms 6848 1728 5120
Eisenstein series 128 0 128

Trace form

\( 1728 q + 8 q^{2} + 4 q^{3} + 864 q^{4} + 16 q^{5} + 60 q^{6} - 64 q^{8} + 148 q^{9} + O(q^{10}) \) \( 1728 q + 8 q^{2} + 4 q^{3} + 864 q^{4} + 16 q^{5} + 60 q^{6} - 64 q^{8} + 148 q^{9} + 42 q^{11} - 96 q^{12} + 388 q^{15} + 3456 q^{16} - 152 q^{17} - 552 q^{18} - 540 q^{19} + 64 q^{20} - 224 q^{21} - 36 q^{22} + 1856 q^{23} + 240 q^{24} + 5112 q^{25} - 368 q^{27} + 584 q^{29} - 936 q^{30} - 72 q^{31} - 512 q^{32} + 720 q^{33} + 360 q^{34} - 560 q^{35} + 648 q^{36} - 288 q^{37} + 496 q^{38} + 256 q^{39} - 20 q^{41} + 684 q^{43} + 1664 q^{44} + 2240 q^{45} - 1244 q^{47} - 320 q^{48} + 10584 q^{49} + 1400 q^{50} - 2550 q^{51} + 136 q^{53} + 3272 q^{54} - 3376 q^{57} + 1630 q^{59} - 880 q^{60} - 27648 q^{64} - 5144 q^{65} + 640 q^{66} - 3348 q^{67} + 304 q^{68} - 3708 q^{69} + 1312 q^{71} - 736 q^{72} + 1656 q^{73} + 1744 q^{74} + 310 q^{75} - 720 q^{76} + 4384 q^{78} - 1872 q^{79} - 512 q^{80} - 5380 q^{81} + 6264 q^{82} - 4100 q^{83} - 2688 q^{84} - 1440 q^{85} - 2836 q^{86} + 3440 q^{87} - 144 q^{88} + 12720 q^{89} + 3760 q^{90} - 3024 q^{91} - 1856 q^{92} + 16956 q^{93} + 4128 q^{95} + 1280 q^{96} + 2250 q^{97} + 3136 q^{98} + 6884 q^{99} + O(q^{100}) \)

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

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