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Properties

Label 1386.4.w
Level $1386$
Weight $4$
Character orbit 1386.w
Rep. character $\chi_{1386}(353,\cdot)$
Character field $\Q(\zeta_{6})$
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.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 480 q - 1920 q^{4} + 24 q^{7} - 56 q^{9} + O(q^{10}) \) \( 480 q - 1920 q^{4} + 24 q^{7} - 56 q^{9} - 144 q^{13} + 264 q^{14} - 344 q^{15} + 7680 q^{16} - 288 q^{17} - 16 q^{18} - 56 q^{21} - 312 q^{23} - 6000 q^{25} + 828 q^{27} - 96 q^{28} - 84 q^{29} - 720 q^{30} + 224 q^{36} + 336 q^{37} + 1396 q^{39} + 1236 q^{41} - 576 q^{42} + 84 q^{43} + 660 q^{45} + 504 q^{46} - 792 q^{47} + 84 q^{49} - 2256 q^{50} + 2776 q^{51} + 576 q^{52} - 2112 q^{53} - 360 q^{54} - 1056 q^{56} + 4136 q^{57} + 1376 q^{60} - 5904 q^{62} + 4156 q^{63} - 30720 q^{64} - 2352 q^{67} + 1152 q^{68} - 3696 q^{69} + 720 q^{70} + 64 q^{72} - 2520 q^{74} - 396 q^{75} - 4032 q^{78} + 1680 q^{79} - 8 q^{81} + 224 q^{84} + 1200 q^{86} + 7272 q^{87} + 636 q^{89} + 12168 q^{90} + 180 q^{91} + 1248 q^{92} - 1264 q^{93} - 3168 q^{97} + O(q^{100}) \)

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

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