Properties

Label 3744.1.l
Level $3744$
Weight $1$
Character orbit 3744.l
Rep. character $\chi_{3744}(3041,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
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.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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 68 12 56
Cusp forms 36 12 24
Eisenstein series 32 0 32

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

\( 12q + O(q^{10}) \) \( 12q - 4q^{25} - 4q^{49} + 8q^{61} + O(q^{100}) \)

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.l.a \(4\) \(1.868\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{11}-q^{13}+(-\zeta_{8}+\cdots)q^{17}+\cdots\)
3744.1.l.b \(4\) \(1.868\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{13}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{17}+\cdots\)
3744.1.l.c \(4\) \(1.868\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)