Properties

Label 1386.2.bj
Level $1386$
Weight $2$
Character orbit 1386.bj
Rep. character $\chi_{1386}(659,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
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 592 144 448
Cusp forms 560 144 416
Eisenstein series 32 0 32

Trace form

\( 144q - 8q^{3} - 72q^{4} - 12q^{5} + 24q^{9} + O(q^{10}) \) \( 144q - 8q^{3} - 72q^{4} - 12q^{5} + 24q^{9} - 18q^{11} + 4q^{12} - 20q^{15} - 72q^{16} + 12q^{20} + 6q^{22} + 60q^{25} - 32q^{27} + 12q^{31} - 6q^{33} + 12q^{34} - 12q^{36} - 24q^{37} + 60q^{38} - 48q^{45} + 12q^{47} + 4q^{48} + 72q^{49} + 96q^{59} - 8q^{60} + 144q^{64} + 32q^{66} + 40q^{69} + 20q^{75} - 48q^{78} + 64q^{81} + 24q^{82} - 108q^{86} + 6q^{88} + 48q^{91} - 84q^{93} - 20q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)