Properties

Label 1386.2.cl
Level $1386$
Weight $2$
Character orbit 1386.cl
Rep. character $\chi_{1386}(481,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
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.cl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2368 768 1600
Cusp forms 2240 768 1472
Eisenstein series 128 0 128

Trace form

\( 768q + 192q^{4} + 12q^{9} + O(q^{10}) \) \( 768q + 192q^{4} + 12q^{9} + 4q^{11} + 12q^{15} - 192q^{16} + 12q^{23} - 96q^{25} + 36q^{26} + 54q^{27} - 50q^{35} + 8q^{36} + 20q^{39} - 180q^{41} - 40q^{42} - 4q^{44} - 48q^{45} + 40q^{51} + 52q^{53} + 40q^{57} - 18q^{58} + 8q^{60} - 110q^{63} + 192q^{64} - 24q^{66} + 12q^{70} + 32q^{71} - 40q^{72} - 84q^{75} + 30q^{77} + 48q^{78} + 52q^{81} - 20q^{84} + 8q^{86} + 60q^{89} + 18q^{92} + 66q^{93} - 160q^{95} + 114q^{99} + O(q^{100}) \)

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

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