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Properties

Label 1386.4.cs
Level $1386$
Weight $4$
Character orbit 1386.cs
Rep. character $\chi_{1386}(5,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2304$
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.cs (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 6976 2304 4672
Cusp forms 6848 2304 4544
Eisenstein series 128 0 128

Trace form

\( 2304 q + 2304 q^{4} + 96 q^{9} + O(q^{10}) \) \( 2304 q + 2304 q^{4} + 96 q^{9} + 24 q^{11} - 120 q^{15} - 9216 q^{16} - 224 q^{18} - 280 q^{21} - 504 q^{23} + 7200 q^{25} + 360 q^{26} - 108 q^{27} - 2340 q^{35} + 256 q^{36} - 660 q^{39} - 784 q^{42} - 96 q^{44} - 1392 q^{45} - 672 q^{50} - 2096 q^{51} - 3276 q^{53} - 952 q^{57} - 756 q^{58} + 6000 q^{59} - 320 q^{60} + 2820 q^{63} + 36864 q^{64} + 1200 q^{66} - 72 q^{70} - 1344 q^{72} - 16296 q^{75} - 6420 q^{77} + 4960 q^{78} + 3240 q^{79} + 3872 q^{81} + 720 q^{84} - 1440 q^{85} + 1200 q^{86} - 8784 q^{87} + 8160 q^{89} - 3024 q^{92} - 6296 q^{93} + 2208 q^{98} - 10604 q^{99} + O(q^{100}) \)

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

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