Space of modular forms of level 273, weight 1, and Character 273.o

• Label: 273.1.o
• Level: $273$
• Weight: $1$
• Character orbit: 273.o
• Rep. character: $\chi_{273}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $37$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	273.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(37\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(273, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.1.o.a	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{3}+iq^{4}-iq^{7}-q^{9}-q^{12}+\cdots\)
273.1.o.b	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-iq^{3}+iq^{4}+q^{7}-q^{9}+q^{12}-iq^{13}+\cdots\)