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

• Label: 3675.1.bf
• Level: $3675$
• Weight: $1$
• Character orbit: 3675.bf
• Rep. character: $\chi_{3675}(68,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $560$
• Trace bound: $61$

Defining parameters

Level:	\( N \)	\(=\)	\( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3675.bf (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(560\)
Trace bound:			\(61\)

Dimensions

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

	Total	New	Old
Modular forms	256	80	176
Cusp forms	64	48	16
Eisenstein series	192	32	160

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q + 24 q^{16} - 48 q^{36} + 12 q^{61} + 24 q^{81}+O(q^{100}) \)

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.bf.a	$3675$	$1$	3675.bf	105.w	$12$	$8$	$2$	$1.834$	\(\Q(\zeta_{24})\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \)	\(\Q(\sqrt{105}) \)					525.1.k.a	$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{9}+\cdots\)
3675.1.bf.b	$3675$	$1$	3675.bf	105.w	$12$	$8$	$2$	$1.834$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None					525.1.be.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{9}+\cdots\)
3675.1.bf.c	$3675$	$1$	3675.bf	105.w	$12$	$16$	$4$	$1.834$	\(\Q(\zeta_{48})\)	$D_{8}$	\(\Q(\sqrt{-15}) \)	None		✓			3675.1.k.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(\zeta_{48}^{5}-\zeta_{48}^{23})q^{2}-\zeta_{48}^{10}q^{3}+\cdots\)
3675.1.bf.d	$3675$	$1$	3675.bf	105.w	$12$	$16$	$4$	$1.834$	\(\Q(\zeta_{48})\)	$D_{8}$	\(\Q(\sqrt{-15}) \)	None		✓			3675.1.k.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(\zeta_{48}^{7}+\zeta_{48}^{13})q^{2}-\zeta_{48}^{2}q^{3}+(-\zeta_{48}^{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3675, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)