Properties

Label 1386.2.bu
Level $1386$
Weight $2$
Character orbit 1386.bu
Rep. character $\chi_{1386}(701,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
Newform subspaces $2$
Sturm bound $576$
Trace bound $2$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
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 1216 96 1120
Cusp forms 1088 96 992
Eisenstein series 128 0 128

Trace form

\( 96q - 24q^{4} + O(q^{10}) \) \( 96q - 24q^{4} - 24q^{16} + 8q^{22} + 48q^{25} + 80q^{31} - 32q^{34} + 32q^{37} - 80q^{46} + 24q^{49} - 80q^{52} - 64q^{55} - 32q^{58} + 80q^{61} - 24q^{64} + 96q^{67} + 16q^{70} + 80q^{73} + 80q^{79} - 32q^{82} - 40q^{85} + 8q^{88} - 16q^{97} + O(q^{100}) \)

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.bu.a \(48\) \(11.067\) None \(-12\) \(0\) \(0\) \(0\)
1386.2.bu.b \(48\) \(11.067\) None \(12\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)