Properties

Label 2736.1.b
Level $2736$
Weight $1$
Character orbit 2736.b
Rep. character $\chi_{2736}(2735,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $480$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2736.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 40 12 28
Cusp forms 16 12 4
Eisenstein series 24 0 24

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

\( 12 q + O(q^{10}) \) \( 12 q - 12 q^{25} - 12 q^{49} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2736.1.b.a 2736.b 228.b $4$ $1.365$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
2736.1.b.b 2736.b 228.b $8$ $1.365$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)