Properties

Label 1386.4.m
Level $1386$
Weight $4$
Character orbit 1386.m
Rep. character $\chi_{1386}(379,\cdot)$
Character field $\Q(\zeta_{5})$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 3520 360 3160
Cusp forms 3392 360 3032
Eisenstein series 128 0 128

Trace form

\( 360 q + 4 q^{2} - 360 q^{4} - 16 q^{5} + 16 q^{8} + O(q^{10}) \) \( 360 q + 4 q^{2} - 360 q^{4} - 16 q^{5} + 16 q^{8} + 118 q^{11} + 240 q^{13} - 1440 q^{16} - 12 q^{17} + 174 q^{19} - 64 q^{20} + 36 q^{22} + 1440 q^{23} - 2070 q^{25} - 40 q^{26} - 788 q^{29} + 60 q^{31} - 256 q^{32} + 648 q^{34} + 140 q^{35} - 360 q^{37} - 392 q^{38} + 660 q^{41} + 6268 q^{43} + 672 q^{44} - 368 q^{46} - 1308 q^{47} - 4410 q^{49} + 1516 q^{50} - 1280 q^{52} + 2868 q^{53} - 3320 q^{55} + 1208 q^{58} - 366 q^{59} - 888 q^{61} - 48 q^{62} - 5760 q^{64} - 8744 q^{65} - 2388 q^{67} - 48 q^{68} - 1008 q^{70} + 2724 q^{71} - 2388 q^{73} + 2696 q^{74} - 1104 q^{76} - 224 q^{77} + 1456 q^{79} - 256 q^{80} - 2428 q^{82} + 10998 q^{83} - 8780 q^{85} + 2204 q^{86} + 144 q^{88} + 1812 q^{89} + 1512 q^{91} - 400 q^{92} - 3520 q^{94} - 4360 q^{95} + 854 q^{97} - 784 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)