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Properties

Label 1386.2.r
Level $1386$
Weight $2$
Character orbit 1386.r
Rep. character $\chi_{1386}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $4$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 608 48 560
Cusp forms 544 48 496
Eisenstein series 64 0 64

Trace form

\( 48 q + 24 q^{4} + O(q^{10}) \) \( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{19} - 8 q^{25} + 40 q^{37} - 32 q^{43} + 16 q^{46} - 24 q^{58} - 48 q^{61} - 48 q^{64} - 64 q^{67} - 16 q^{70} - 96 q^{73} - 16 q^{79} - 48 q^{82} - 32 q^{85} + 80 q^{91} + 96 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1386.2.r.a 1386.r 21.g $8$ $11.067$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(-2+\zeta_{24}+\cdots)q^{5}+\cdots\)
1386.2.r.b 1386.r 21.g $8$ $11.067$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)
1386.2.r.c 1386.r 21.g $8$ $11.067$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(2+\zeta_{24}-2\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
1386.2.r.d 1386.r 21.g $24$ $11.067$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)