Space of modular forms of level 273, weight 2, and Character 273.c

• Label: 273.2.c
• Level: $273$
• Weight: $2$
• Character orbit: 273.c
• Rep. character: $\chi_{273}(64,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(74\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

	Total	New	Old
Modular forms	40	16	24
Cusp forms	32	16	16
Eisenstein series	8	0	8

Trace form

\( 16 q - 20 q^{4} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.2.c.a	$273$	$2$	273.c	13.b	$2$	$2$	$2$	$2.180$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+q^{3}-2q^{4}+3iq^{5}+2iq^{6}+\cdots\)
273.2.c.b	$273$	$2$	273.c	13.b	$2$	$6$	$6$	$2.180$	6.0.350464.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
273.2.c.c	$273$	$2$	273.c	13.b	$2$	$8$	$8$	$2.180$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \)