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Properties

Label 1386.4.cz
Level $1386$
Weight $4$
Character orbit 1386.cz
Rep. character $\chi_{1386}(95,\cdot)$
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.cz (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

\( 2304 q + 1152 q^{4} - 96 q^{9} + O(q^{10}) \) \( 2304 q + 1152 q^{4} - 96 q^{9} + 120 q^{15} + 4608 q^{16} + 14400 q^{25} - 360 q^{26} - 36 q^{27} - 1596 q^{33} - 3900 q^{35} + 256 q^{36} - 460 q^{39} - 1304 q^{42} + 96 q^{44} + 1088 q^{45} + 260 q^{51} - 3276 q^{53} + 612 q^{55} + 280 q^{57} - 1512 q^{58} + 3000 q^{59} + 640 q^{60} + 5540 q^{63} - 36864 q^{64} - 1728 q^{66} + 3440 q^{69} - 72 q^{70} + 1120 q^{72} - 5224 q^{75} + 3276 q^{77} + 4960 q^{78} - 6812 q^{81} - 400 q^{84} + 8160 q^{89} + 8480 q^{90} + 3024 q^{92} + 12368 q^{93} + 20640 q^{95} + 15212 q^{99} + O(q^{100}) \)

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

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