↑

Properties

Label 1386.4.n
Level $1386$
Weight $4$
Character orbit 1386.n
Rep. character $\chi_{1386}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1386.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
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 576 1168
Cusp forms 1712 576 1136
Eisenstein series 32 0 32

Trace form

\( 576 q + 1152 q^{4} - 64 q^{9} + O(q^{10}) \) \( 576 q + 1152 q^{4} - 64 q^{9} - 16 q^{11} + 80 q^{15} - 4608 q^{16} - 336 q^{23} - 14400 q^{25} + 240 q^{26} + 72 q^{27} - 1332 q^{33} + 256 q^{36} - 144 q^{42} - 32 q^{44} - 392 q^{53} - 1008 q^{58} - 3000 q^{59} + 640 q^{60} - 36864 q^{64} - 2016 q^{66} + 72 q^{70} + 48 q^{71} - 5640 q^{75} - 2068 q^{77} - 1408 q^{78} + 1560 q^{81} - 800 q^{86} - 8160 q^{89} - 672 q^{92} - 10944 q^{93} - 4652 q^{99} + O(q^{100}) \)

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

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