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Properties

Label 1386.4.k
Level $1386$
Weight $4$
Character orbit 1386.k
Rep. character $\chi_{1386}(793,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $200$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 1760 200 1560
Cusp forms 1696 200 1496
Eisenstein series 64 0 64

Trace form

\( 200 q - 400 q^{4} + 20 q^{5} - 4 q^{7} + O(q^{10}) \) \( 200 q - 400 q^{4} + 20 q^{5} - 4 q^{7} + 280 q^{13} + 176 q^{14} - 1600 q^{16} - 96 q^{17} + 52 q^{19} - 160 q^{20} - 280 q^{23} - 2628 q^{25} + 312 q^{26} - 64 q^{28} - 440 q^{29} + 784 q^{34} - 856 q^{35} + 448 q^{37} + 632 q^{38} - 1080 q^{41} - 2240 q^{43} + 744 q^{46} + 52 q^{47} - 1432 q^{49} + 3200 q^{50} - 560 q^{52} + 768 q^{53} - 352 q^{56} - 232 q^{58} - 196 q^{59} + 1492 q^{61} - 1968 q^{62} + 12800 q^{64} - 520 q^{65} - 964 q^{67} - 384 q^{68} + 2440 q^{70} - 736 q^{71} - 1292 q^{73} + 792 q^{74} - 416 q^{76} + 176 q^{77} - 2004 q^{79} + 320 q^{80} - 1712 q^{82} - 4768 q^{83} + 5056 q^{85} + 1736 q^{86} + 3012 q^{89} - 992 q^{91} + 2240 q^{92} + 2544 q^{94} + 836 q^{95} - 2200 q^{97} - 1920 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)