Properties

Label 1386.2.l
Level $1386$
Weight $2$
Character orbit 1386.l
Rep. character $\chi_{1386}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 160 432
Cusp forms 560 160 400
Eisenstein series 32 0 32

Trace form

\( 160q - 80q^{4} - 16q^{5} + 8q^{6} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 160q - 80q^{4} - 16q^{5} + 8q^{6} + 4q^{7} - 4q^{9} - 4q^{13} - 4q^{14} - 28q^{15} - 80q^{16} + 12q^{17} - 16q^{18} + 8q^{19} + 8q^{20} + 8q^{21} + 16q^{23} - 4q^{24} + 160q^{25} + 24q^{26} + 12q^{27} + 4q^{28} + 4q^{29} - 20q^{30} - 4q^{31} + 48q^{35} + 8q^{36} - 4q^{37} - 48q^{38} + 32q^{39} + 4q^{41} - 12q^{42} - 4q^{43} - 16q^{45} + 12q^{46} + 12q^{47} + 28q^{49} - 8q^{50} + 4q^{51} + 8q^{52} - 16q^{53} - 4q^{54} + 8q^{56} + 24q^{59} - 4q^{60} - 16q^{61} - 24q^{62} - 32q^{63} + 160q^{64} + 20q^{65} - 28q^{67} - 24q^{68} - 12q^{69} - 12q^{70} - 88q^{71} + 8q^{72} + 56q^{73} - 24q^{74} + 104q^{75} + 8q^{76} - 32q^{78} - 4q^{79} + 8q^{80} + 4q^{81} - 56q^{83} - 28q^{84} + 32q^{86} + 48q^{87} + 52q^{89} - 36q^{90} + 32q^{91} - 8q^{92} - 52q^{93} - 24q^{94} + 28q^{95} - 4q^{96} - 4q^{97} + 48q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)