Properties

Label 1386.2.by
Level $1386$
Weight $2$
Character orbit 1386.by
Rep. character $\chi_{1386}(169,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $576$
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.by (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2368 576 1792
Cusp forms 2240 576 1664
Eisenstein series 128 0 128

Trace form

\( 576q - 4q^{2} - 8q^{3} + 72q^{4} + 4q^{5} + 6q^{6} + 8q^{8} - 32q^{9} + O(q^{10}) \) \( 576q - 4q^{2} - 8q^{3} + 72q^{4} + 4q^{5} + 6q^{6} + 8q^{8} - 32q^{9} + 6q^{11} + 24q^{12} + 16q^{15} + 72q^{16} - 8q^{17} - 12q^{18} + 36q^{19} + 4q^{20} - 8q^{21} + 6q^{22} + 32q^{23} + 6q^{24} + 84q^{25} + 64q^{27} - 76q^{29} + 36q^{30} + 12q^{31} + 16q^{32} - 12q^{33} + 12q^{34} + 16q^{35} + 6q^{36} - 24q^{37} - 32q^{38} + 4q^{39} + 4q^{41} + 12q^{43} + 8q^{44} + 80q^{45} - 44q^{47} + 4q^{48} + 72q^{49} - 28q^{50} + 66q^{51} - 8q^{53} + 20q^{54} - 40q^{57} - 38q^{59} - 16q^{60} - 144q^{64} + 160q^{65} - 32q^{66} - 36q^{67} + 4q^{68} - 56q^{71} - 4q^{72} - 24q^{73} - 8q^{74} + 34q^{75} + 12q^{76} - 128q^{78} + 24q^{79} - 8q^{80} + 8q^{81} + 36q^{82} + 16q^{83} - 24q^{84} + 24q^{85} - 34q^{86} - 40q^{87} + 6q^{88} - 384q^{89} - 56q^{90} + 72q^{91} - 8q^{92} - 120q^{93} - 48q^{95} + 8q^{96} - 6q^{97} - 32q^{98} - 184q^{99} + O(q^{100}) \)

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

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