Properties

Label 3744.1.gs
Level $3744$
Weight $1$
Character orbit 3744.gs
Rep. character $\chi_{3744}(865,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $12$
Newform subspaces $3$
Sturm bound $672$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3744.gs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(672\)
Trace bound: \(17\)

Dimensions

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

Total New Old
Modular forms 176 12 164
Cusp forms 48 12 36
Eisenstein series 128 0 128

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

\( 12q + 2q^{5} + O(q^{10}) \) \( 12q + 2q^{5} - 6q^{37} + 4q^{41} - 4q^{53} - 6q^{61} + 4q^{65} + 2q^{73} - 10q^{85} - 2q^{89} + 2q^{97} + O(q^{100}) \)

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.gs.a \(4\) \(1.868\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{5}-\zeta_{12}q^{13}+(1-\zeta_{12}^{4}+\cdots)q^{17}+\cdots\)
3744.1.gs.b \(4\) \(1.868\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}q^{13}+(-1+\cdots)q^{17}+\cdots\)
3744.1.gs.c \(4\) \(1.868\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}^{4}-\zeta_{12}^{5})q^{5}+\zeta_{12}q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1872, [\chi])\)\(^{\oplus 2}\)