Properties

Label 2736.1.bs
Level $2736$
Weight $1$
Character orbit 2736.bs
Rep. character $\chi_{2736}(1633,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $480$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2736.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(480\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2736, [\chi])\).

Total New Old
Modular forms 48 8 40
Cusp forms 24 4 20
Eisenstein series 24 4 20

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4q - 2q^{5} + 2q^{7} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{5} + 2q^{7} - 4q^{9} - 2q^{11} - 2q^{23} - 4q^{35} + 2q^{39} + 2q^{43} + 2q^{45} + 2q^{47} + 4q^{55} - 4q^{57} + 2q^{61} - 2q^{63} + 2q^{77} + 4q^{81} - 2q^{83} - 2q^{87} + 2q^{93} + 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2736.1.bs.a \(4\) \(1.365\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(-2\) \(2\) \(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)