Space of modular forms of level 3675, weight 1, and Character 3675.cl

• Label: 3675.1.cl
• Level: $3675$
• Weight: $1$
• Character orbit: 3675.cl
• Rep. character: $\chi_{3675}(74,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $560$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3675.cl (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 735 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(560\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3675, [\chi])\).

	Total	New	Old
Modular forms	168	72	96
Cusp forms	24	24	0
Eisenstein series	144	48	96

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

\( 24 q - 2 q^{4} - 2 q^{9} + 2 q^{16} + 2 q^{19} + 2 q^{21} + 4 q^{31} - 4 q^{36} - 26 q^{39} - 2 q^{49} + 26 q^{61} + 4 q^{64} + 4 q^{76} + 2 q^{79} + 2 q^{81} + 4 q^{84} - 2 q^{91}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3675, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3675.1.cl.a	$3675$	$1$	3675.cl	735.aq	$42$	$24$	$2$	$1.834$	\(\Q(\zeta_{84})\)	$D_{21}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	3675.1.cg.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{84}^{25}q^{3}-\zeta_{84}^{40}q^{4}-\zeta_{84}^{13}q^{7}+\cdots\)