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Properties

Label 1386.2.bf
Level $1386$
Weight $2$
Character orbit 1386.bf
Rep. character $\chi_{1386}(769,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

Total New Old
Modular forms 592 192 400
Cusp forms 560 192 368
Eisenstein series 32 0 32

Trace form

\( 192 q + 96 q^{4} - 16 q^{9} + O(q^{10}) \) \( 192 q + 96 q^{4} - 16 q^{9} - 4 q^{11} + 8 q^{15} - 96 q^{16} + 24 q^{23} + 96 q^{25} - 8 q^{36} - 24 q^{42} - 8 q^{44} - 128 q^{53} + 24 q^{58} - 8 q^{60} - 192 q^{64} - 12 q^{70} - 48 q^{71} - 34 q^{77} - 16 q^{78} - 24 q^{81} - 8 q^{86} - 24 q^{92} - 48 q^{93} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

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