Properties

Label 1386.2.cs
Level $1386$
Weight $2$
Character orbit 1386.cs
Rep. character $\chi_{1386}(5,\cdot)$
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.cs (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

\( 768q + 192q^{4} - 12q^{9} + O(q^{10}) \) \( 768q + 192q^{4} - 12q^{9} - 12q^{11} - 12q^{15} - 192q^{16} + 16q^{18} + 20q^{21} + 36q^{23} + 96q^{25} + 36q^{26} + 54q^{27} + 90q^{35} - 8q^{36} - 40q^{42} + 12q^{44} + 48q^{45} + 48q^{50} - 44q^{51} - 36q^{53} + 44q^{57} + 18q^{58} - 120q^{59} - 8q^{60} - 30q^{63} + 192q^{64} - 24q^{66} + 12q^{70} + 24q^{72} + 84q^{75} + 42q^{77} - 80q^{78} - 72q^{79} - 28q^{81} + 24q^{85} - 24q^{86} - 288q^{87} + 60q^{89} + 54q^{92} - 2q^{93} + 48q^{98} + 142q^{99} + O(q^{100}) \)

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

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