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Properties

Label 1386.4.l
Level $1386$
Weight $4$
Character orbit 1386.l
Rep. character $\chi_{1386}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $480$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 480 1264
Cusp forms 1712 480 1232
Eisenstein series 32 0 32

Trace form

\( 480 q - 960 q^{4} + 80 q^{5} - 16 q^{6} - 24 q^{7} - 28 q^{9} + O(q^{10}) \) \( 480 q - 960 q^{4} + 80 q^{5} - 16 q^{6} - 24 q^{7} - 28 q^{9} - 48 q^{13} - 88 q^{14} + 344 q^{15} - 3840 q^{16} - 96 q^{17} + 32 q^{18} + 240 q^{19} - 160 q^{20} + 356 q^{21} + 208 q^{23} + 32 q^{24} + 12000 q^{25} - 624 q^{26} + 804 q^{27} - 96 q^{28} + 28 q^{29} + 184 q^{30} + 60 q^{31} + 1128 q^{35} + 224 q^{36} - 336 q^{37} + 1824 q^{38} - 352 q^{39} + 412 q^{41} + 888 q^{42} - 84 q^{43} - 1132 q^{45} - 504 q^{46} - 132 q^{47} - 312 q^{49} - 752 q^{50} - 1388 q^{51} + 384 q^{52} + 704 q^{53} + 1016 q^{54} + 704 q^{56} + 3288 q^{57} - 1416 q^{59} + 320 q^{60} + 1716 q^{61} - 1968 q^{62} + 3352 q^{63} + 30720 q^{64} - 1336 q^{65} + 1176 q^{67} + 768 q^{68} + 3744 q^{69} - 360 q^{70} - 4336 q^{71} - 64 q^{72} - 1344 q^{73} - 1680 q^{74} + 1184 q^{75} + 960 q^{76} - 1664 q^{78} - 840 q^{79} - 640 q^{80} + 2140 q^{81} + 112 q^{83} - 2032 q^{84} + 3008 q^{86} + 7464 q^{87} - 4484 q^{89} + 72 q^{90} + 1500 q^{91} - 416 q^{92} + 2744 q^{93} - 2448 q^{94} + 4252 q^{95} + 128 q^{96} - 1056 q^{97} - 2976 q^{98} + O(q^{100}) \)

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

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