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Properties

Label 1386.4.db
Level $1386$
Weight $4$
Character orbit 1386.db
Rep. character $\chi_{1386}(61,\cdot)$
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.db (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

\( 2304 q - 1152 q^{4} - 96 q^{9} + O(q^{10}) \) \( 2304 q - 1152 q^{4} - 96 q^{9} + 16 q^{11} + 120 q^{15} + 4608 q^{16} + 336 q^{23} + 14400 q^{25} + 360 q^{26} + 108 q^{27} - 3468 q^{33} + 1300 q^{35} - 256 q^{36} - 460 q^{39} + 7200 q^{41} + 1304 q^{42} + 32 q^{44} - 260 q^{51} + 2212 q^{53} + 280 q^{57} - 1512 q^{58} + 3000 q^{59} - 640 q^{60} - 5540 q^{63} + 36864 q^{64} - 2064 q^{66} - 72 q^{70} - 2848 q^{71} - 1120 q^{72} + 5640 q^{75} - 612 q^{77} - 4512 q^{78} - 260 q^{81} + 400 q^{84} + 800 q^{86} + 8160 q^{89} - 1008 q^{92} - 816 q^{93} - 6880 q^{95} - 11028 q^{99} + O(q^{100}) \)

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

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