Space of modular forms of level 3672, weight 1, and Character 3672.dp

• Label: 3672.1.dp
• Level: $3672$
• Weight: $1$
• Character orbit: 3672.dp
• Rep. character: $\chi_{3672}(115,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $648$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3672 = 2^{3} \cdot 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3672.dp (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3672 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(648\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3672, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	24	24	0
Eisenstein series	48	48	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3672, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3672.1.dp.a	$3672$	$1$	3672.dp	3672.cp	$36$	$12$	$1$	$1.833$	\(\Q(\zeta_{36})\)	$D_{36}$	\(\Q(\sqrt{-2}) \)	None		✓			3672.1.dp.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{36}^{7}q^{2}+\zeta_{36}^{10}q^{3}+\zeta_{36}^{14}q^{4}+\cdots\)
3672.1.dp.b	$3672$	$1$	3672.dp	3672.cp	$36$	$12$	$1$	$1.833$	\(\Q(\zeta_{36})\)	$D_{36}$	\(\Q(\sqrt{-2}) \)	None		✓			3672.1.dp.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{36}^{7}q^{2}+\zeta_{36}q^{3}+\zeta_{36}^{14}q^{4}+\cdots\)