Properties

Label 2736.1.ga
Level $2736$
Weight $1$
Character orbit 2736.ga
Rep. character $\chi_{2736}(271,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $12$
Newform subspaces $2$
Sturm bound $480$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2736.ga (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(19\)

Dimensions

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

Total New Old
Modular forms 156 12 144
Cusp forms 12 12 0
Eisenstein series 144 0 144

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q + O(q^{10}) \) \( 12q + 6q^{13} + 6q^{49} + 12q^{61} + 6q^{73} + O(q^{100}) \)

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.ga.a \(6\) \(1.365\) \(\Q(\zeta_{18})\) \(D_{18}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)
2736.1.ga.b \(6\) \(1.365\) \(\Q(\zeta_{18})\) \(D_{18}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}^{7}-\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)