Properties

Label 1386.2.cf
Level $1386$
Weight $2$
Character orbit 1386.cf
Rep. character $\chi_{1386}(29,\cdot)$
Character field $\Q(\zeta_{30})$
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.cf (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 576q + 8q^{3} + 72q^{4} + 12q^{5} - 10q^{6} + 16q^{9} + O(q^{10}) \) \( 576q + 8q^{3} + 72q^{4} + 12q^{5} - 10q^{6} + 16q^{9} + 18q^{11} - 24q^{12} + 72q^{16} + 20q^{18} - 60q^{19} - 12q^{20} - 6q^{22} + 10q^{24} - 60q^{25} + 32q^{27} + 180q^{29} + 60q^{30} - 12q^{31} - 4q^{33} - 12q^{34} + 22q^{36} + 24q^{37} + 120q^{38} + 100q^{39} + 48q^{45} - 12q^{47} - 4q^{48} - 72q^{49} - 10q^{51} + 20q^{57} + 114q^{59} + 8q^{60} - 144q^{64} - 32q^{66} + 60q^{67} + 40q^{69} + 50q^{75} + 128q^{78} - 104q^{81} + 36q^{82} - 180q^{83} - 40q^{84} - 102q^{86} - 6q^{88} - 200q^{90} + 72q^{91} - 176q^{93} - 240q^{95} + 30q^{97} + 220q^{99} + O(q^{100}) \)

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

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