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Properties

Label 1386.2.y
Level $1386$
Weight $2$
Character orbit 1386.y
Rep. character $\chi_{1386}(419,\cdot)$
Character field $\Q(\zeta_{6})$
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.y (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 160 q + 80 q^{4} - 4 q^{7} - 8 q^{9} + O(q^{10}) \) \( 160 q + 80 q^{4} - 4 q^{7} - 8 q^{9} + 12 q^{14} - 8 q^{15} - 80 q^{16} + 8 q^{18} - 32 q^{21} + 24 q^{23} - 80 q^{25} - 8 q^{28} + 24 q^{29} + 48 q^{30} - 16 q^{36} + 16 q^{37} + 16 q^{39} - 8 q^{43} - 48 q^{46} + 16 q^{49} - 24 q^{50} + 40 q^{51} + 12 q^{56} - 88 q^{57} - 40 q^{60} - 20 q^{63} - 160 q^{64} - 192 q^{65} + 56 q^{67} - 12 q^{70} + 16 q^{72} - 72 q^{74} + 8 q^{79} + 16 q^{81} - 16 q^{84} + 24 q^{86} - 48 q^{91} + 24 q^{92} + 176 q^{93} + 72 q^{95} + O(q^{100}) \)

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

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