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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

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

Display 100 coefficients 10 coefficients

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

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