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Properties

Label 1386.2.db
Level $1386$
Weight $2$
Character orbit 1386.db
Rep. character $\chi_{1386}(61,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
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.db (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
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 768 1600
Cusp forms 2240 768 1472
Eisenstein series 128 0 128

Trace form

\( 768 q - 96 q^{4} + 12 q^{9} + O(q^{10}) \) \( 768 q - 96 q^{4} + 12 q^{9} - 8 q^{11} + 12 q^{15} + 96 q^{16} - 24 q^{23} + 192 q^{25} + 36 q^{26} - 54 q^{27} + 132 q^{33} - 50 q^{35} + 8 q^{36} + 20 q^{39} + 180 q^{41} - 4 q^{42} - 4 q^{44} - 20 q^{51} + 52 q^{53} + 40 q^{57} + 36 q^{58} - 60 q^{59} - 16 q^{60} + 10 q^{63} + 192 q^{64} - 120 q^{66} + 12 q^{70} + 32 q^{71} + 20 q^{72} + 60 q^{75} - 54 q^{77} + 48 q^{78} - 104 q^{81} - 20 q^{84} - 16 q^{86} + 60 q^{89} + 18 q^{92} - 132 q^{93} + 80 q^{95} + 114 q^{99} + O(q^{100}) \)

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

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