Space of modular forms of level 73, weight 2, and trivial character

• Label: 73.2.a
• Level: $73$
• Weight: $2$
• Character orbit: 73.a
• Rep. character: $\chi_{73}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(73))\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	5	5	0
Eisenstein series	1	1	0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(73\)	Dim
\(+\)	\(2\)
\(-\)	\(3\)

Trace form

\( 5 q - q^{2} - 2 q^{3} + 5 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{7} - 3 q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(73))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		73
73.2.a.a	$73$	$2$	73.a	1.a	$1$	$1$	$1$	$0.583$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}+2q^{7}-3q^{8}-3q^{9}+\cdots\)
73.2.a.b	$73$	$2$	73.a	1.a	$1$	$2$	$2$	$0.583$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-3\)	\(-3\)	\(-6\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
73.2.a.c	$73$	$2$	73.a	1.a	$1$	$2$	$2$	$0.583$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\)