Properties

Label 1386.2.cz
Level $1386$
Weight $2$
Character orbit 1386.cz
Rep. character $\chi_{1386}(95,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
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.cz (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

\( 768q + 96q^{4} + 12q^{9} + O(q^{10}) \) \( 768q + 96q^{4} + 12q^{9} + 12q^{15} + 96q^{16} + 192q^{25} - 36q^{26} + 18q^{27} + 24q^{33} + 150q^{35} - 8q^{36} + 20q^{39} + 4q^{42} - 12q^{44} + 8q^{45} + 20q^{51} - 36q^{53} - 12q^{55} + 40q^{57} + 36q^{58} - 60q^{59} + 16q^{60} - 10q^{63} - 192q^{64} - 48q^{66} - 136q^{69} + 12q^{70} - 20q^{72} + 116q^{75} + 90q^{77} - 80q^{78} + 112q^{81} + 20q^{84} + 60q^{89} + 80q^{90} - 54q^{92} - 28q^{93} - 240q^{95} - 94q^{99} + O(q^{100}) \)

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

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