Properties

Label 2736.1.bk
Level $2736$
Weight $1$
Character orbit 2736.bk
Rep. character $\chi_{2736}(847,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
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 76 4 72
Cusp forms 28 4 24
Eisenstein series 48 0 48

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

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

Trace form

\( 4q + O(q^{10}) \) \( 4q - 2q^{13} + 2q^{25} - 4q^{37} - 8q^{49} + 2q^{61} - 2q^{73} + 4q^{97} + O(q^{100}) \)

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.bk.a \(2\) \(1.365\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}-q^{19}+\cdots\)
2736.1.bk.b \(2\) \(1.365\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)