Properties

Label 1386.2.i
Level $1386$
Weight $2$
Character orbit 1386.i
Rep. character $\chi_{1386}(529,\cdot)$
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.i (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

\( 160q + 160q^{4} + 8q^{5} + 8q^{6} + 4q^{7} + 8q^{9} + O(q^{10}) \) \( 160q + 160q^{4} + 8q^{5} + 8q^{6} + 4q^{7} + 8q^{9} - 4q^{13} - 4q^{14} - 28q^{15} + 160q^{16} + 12q^{17} + 8q^{18} + 8q^{19} + 8q^{20} + 20q^{21} - 8q^{23} + 8q^{24} - 80q^{25} + 24q^{26} + 12q^{27} + 4q^{28} + 4q^{29} - 8q^{30} + 8q^{31} + 48q^{35} + 8q^{36} - 4q^{37} + 24q^{38} - 28q^{39} + 4q^{41} + 24q^{42} - 4q^{43} + 20q^{45} + 12q^{46} - 24q^{47} - 8q^{49} - 8q^{50} - 8q^{51} - 4q^{52} - 16q^{53} - 28q^{54} - 4q^{56} - 48q^{59} - 28q^{60} + 32q^{61} - 24q^{62} - 68q^{63} + 160q^{64} - 40q^{65} + 56q^{67} + 12q^{68} - 12q^{69} + 24q^{70} - 88q^{71} + 8q^{72} + 56q^{73} + 12q^{74} - 100q^{75} + 8q^{76} - 32q^{78} + 8q^{79} + 8q^{80} - 8q^{81} - 56q^{83} + 20q^{84} - 16q^{86} - 60q^{87} + 52q^{89} - 36q^{90} + 32q^{91} - 8q^{92} + 56q^{93} + 48q^{94} - 56q^{95} + 8q^{96} - 4q^{97} + 48q^{98} + O(q^{100}) \)

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

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