Properties

Label 3744.1.ci
Level $3744$
Weight $1$
Character orbit 3744.ci
Rep. character $\chi_{3744}(1039,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $672$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3744.ci (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 936 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(672\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3744, [\chi])\).

Total New Old
Modular forms 80 20 60
Cusp forms 48 12 36
Eisenstein series 32 8 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

\( 12q + O(q^{10}) \) \( 12q - 6q^{25} + 6q^{27} + 12q^{35} - 6q^{49} + 6q^{51} - 12q^{75} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3744.1.ci.a \(6\) \(1.868\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{2}q^{3}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{5}+(\zeta_{18}^{7}+\cdots)q^{7}+\cdots\)
3744.1.ci.b \(6\) \(1.868\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{5}q^{3}+(\zeta_{18}-\zeta_{18}^{2})q^{5}+(\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)