Properties

Label 1386.2.ba
Level $1386$
Weight $2$
Character orbit 1386.ba
Rep. character $\chi_{1386}(989,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
Sturm bound $576$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 608 64 544
Cusp forms 544 64 480
Eisenstein series 64 0 64

Trace form

\( 64q - 32q^{4} + O(q^{10}) \) \( 64q - 32q^{4} - 32q^{16} + 8q^{22} + 8q^{25} + 8q^{31} + 16q^{34} + 8q^{37} + 40q^{49} - 24q^{55} + 16q^{58} + 64q^{64} - 16q^{67} - 8q^{70} - 32q^{82} - 4q^{88} - 64q^{97} + O(q^{100}) \)

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.ba.a \(32\) \(11.067\) None \(-16\) \(0\) \(0\) \(0\)
1386.2.ba.b \(32\) \(11.067\) None \(16\) \(0\) \(0\) \(0\)

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

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