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Properties

Label 1386.4.cq
Level $1386$
Weight $4$
Character orbit 1386.cq
Rep. character $\chi_{1386}(335,\cdot)$
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.cq (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

\( 2304 q - 1152 q^{4} - 192 q^{9} + O(q^{10}) \) \( 2304 q - 1152 q^{4} - 192 q^{9} - 24 q^{11} - 120 q^{15} + 4608 q^{16} - 224 q^{18} - 160 q^{21} - 1008 q^{23} + 7200 q^{25} + 256 q^{36} - 2328 q^{39} - 520 q^{42} + 1344 q^{50} - 4148 q^{51} + 1904 q^{57} + 1512 q^{58} - 320 q^{60} - 1428 q^{63} + 36864 q^{64} + 3840 q^{65} - 72 q^{70} - 1344 q^{72} + 6540 q^{77} + 4288 q^{78} - 2376 q^{79} + 3296 q^{81} + 720 q^{84} - 1440 q^{85} - 1200 q^{86} + 6048 q^{92} + 4456 q^{93} - 12384 q^{95} + 30388 q^{99} + O(q^{100}) \)

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

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