Properties

Label 1386.2.n
Level $1386$
Weight $2$
Character orbit 1386.n
Rep. character $\chi_{1386}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $576$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.n (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

\( 192q + 96q^{4} + 8q^{9} + O(q^{10}) \) \( 192q + 96q^{4} + 8q^{9} + 8q^{11} + 8q^{15} - 96q^{16} + 24q^{23} - 192q^{25} + 24q^{26} - 36q^{27} + 18q^{33} - 8q^{36} + 24q^{42} + 4q^{44} - 32q^{53} + 24q^{58} + 60q^{59} + 16q^{60} - 192q^{64} - 12q^{70} + 48q^{71} - 60q^{75} + 14q^{77} + 32q^{78} - 96q^{81} + 16q^{86} - 60q^{89} + 12q^{92} + 72q^{93} + 46q^{99} + O(q^{100}) \)

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

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