Properties

Label 1386.2.cj
Level $1386$
Weight $2$
Character orbit 1386.cj
Rep. character $\chi_{1386}(13,\cdot)$
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.cj (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

\( 768q - 96q^{4} - 24q^{9} + O(q^{10}) \) \( 768q - 96q^{4} - 24q^{9} + 4q^{11} + 12q^{15} + 96q^{16} - 24q^{23} - 96q^{25} + 100q^{35} + 8q^{36} - 40q^{39} + 44q^{42} + 8q^{44} - 20q^{51} + 208q^{53} - 80q^{57} + 36q^{58} + 8q^{60} + 10q^{63} + 192q^{64} + 12q^{70} - 112q^{71} - 40q^{72} - 6q^{77} + 96q^{78} - 56q^{81} - 20q^{84} + 8q^{86} - 36q^{92} - 12q^{93} + 80q^{95} - 336q^{99} + O(q^{100}) \)

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

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