Space of modular forms of level 3549, weight 1, and Character 3549.bs

• Label: 3549.1.bs
• Level: $3549$
• Weight: $1$
• Character orbit: 3549.bs
• Rep. character: $\chi_{3549}(89,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $485$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3549.bs (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(485\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3549, [\chi])\).

	Total	New	Old
Modular forms	132	92	40
Cusp forms	20	12	8
Eisenstein series	112	80	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

\( 12 q + 6 q^{9} - 2 q^{12} - 12 q^{16} + 2 q^{19} + 2 q^{21} + 2 q^{28} + 2 q^{31} - 2 q^{37} + 6 q^{43} - 2 q^{49} + 2 q^{57} - 2 q^{67} - 2 q^{73} - 4 q^{75} - 4 q^{76} - 6 q^{81} - 4 q^{93} - 2 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3549, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3549.1.bs.a	$3549$	$1$	3549.bs	273.as	$12$	$4$	$1$	$1.771$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None					273.1.bs.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}+\zeta_{12}^{4}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
3549.1.bs.b	$3549$	$1$	3549.bs	273.as	$12$	$4$	$1$	$1.771$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None					273.1.bs.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
3549.1.bs.c	$3549$	$1$	3549.bs	273.as	$12$	$4$	$1$	$1.771$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None					273.1.bs.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}^{4}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3549, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)