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Properties

Label 1386.4.cj
Level $1386$
Weight $4$
Character orbit 1386.cj
Rep. character $\chi_{1386}(13,\cdot)$
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.cj (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

\( 2304 q - 1152 q^{4} + 192 q^{9} + O(q^{10}) \) \( 2304 q - 1152 q^{4} + 192 q^{9} - 8 q^{11} + 120 q^{15} + 4608 q^{16} + 336 q^{23} - 7200 q^{25} - 2600 q^{35} - 256 q^{36} + 920 q^{39} - 520 q^{42} - 64 q^{44} - 260 q^{51} + 8848 q^{53} - 560 q^{57} - 1512 q^{58} + 320 q^{60} - 5540 q^{63} + 36864 q^{64} - 72 q^{70} + 2192 q^{71} + 2240 q^{72} - 3876 q^{77} - 5184 q^{78} + 15088 q^{81} + 400 q^{84} - 400 q^{86} + 2016 q^{92} - 10344 q^{93} - 6880 q^{95} + 25764 q^{99} + O(q^{100}) \)

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

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