Properties

Label 1386.2.bk
Level $1386$
Weight $2$
Character orbit 1386.bk
Rep. character $\chi_{1386}(703,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $4$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(576\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

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

Total New Old
Modular forms 608 80 528
Cusp forms 544 80 464
Eisenstein series 64 0 64

Trace form

\( 80q + 40q^{4} - 12q^{5} + O(q^{10}) \) \( 80q + 40q^{4} - 12q^{5} - 8q^{14} - 40q^{16} + 16q^{22} - 8q^{23} + 56q^{25} + 12q^{26} + 12q^{31} - 8q^{37} + 12q^{38} + 24q^{47} - 48q^{49} + 28q^{53} - 4q^{56} - 12q^{58} - 60q^{59} - 80q^{64} + 28q^{67} + 36q^{70} + 104q^{71} - 24q^{77} + 12q^{80} + 48q^{82} + 4q^{86} + 8q^{88} - 24q^{89} + 92q^{91} - 16q^{92} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1386.2.bk.a \(16\) \(11.067\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-12\) \(-6\) \(q-\beta _{12}q^{2}+(1+\beta _{13})q^{4}+(-1-\beta _{9}+\cdots)q^{5}+\cdots\)
1386.2.bk.b \(16\) \(11.067\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-12\) \(6\) \(q+\beta _{12}q^{2}+(1+\beta _{13})q^{4}+(-1-\beta _{9}+\cdots)q^{5}+\cdots\)
1386.2.bk.c \(16\) \(11.067\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(0\) \(q+\beta _{1}q^{2}+\beta _{10}q^{4}+(\beta _{8}+\beta _{10})q^{5}+\cdots\)
1386.2.bk.d \(32\) \(11.067\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)