Space of modular forms of level 752, weight 2, and trivial character

• Label: 752.2.a
• Level: $752$
• Weight: $2$
• Character orbit: 752.a
• Rep. character: $\chi_{752}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $9$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 752 = 2^{4} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	752.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(752))\).

	Total	New	Old
Modular forms	102	23	79
Cusp forms	91	23	68
Eisenstein series	11	0	11

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

\(2\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	$-$	\(8\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(9\)
Minus space		\(-\)	\(14\)

Trace form

\( 23 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 19 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(752))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	47
752.2.a.a	$752$	$2$	752.a	1.a	$1$	$1$	$1$	$6.005$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}-2q^{11}-4q^{13}-2q^{17}+2q^{19}+\cdots\)
752.2.a.b	$752$	$2$	752.a	1.a	$1$	$2$	$2$	$6.005$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-3+\beta )q^{7}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
752.2.a.c	$752$	$2$	752.a	1.a	$1$	$2$	$2$	$6.005$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+(2+\beta )q^{5}+(2-2\beta )q^{7}+5q^{9}+\cdots\)
752.2.a.d	$752$	$2$	752.a	1.a	$1$	$2$	$2$	$6.005$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+(1-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
752.2.a.e	$752$	$2$	752.a	1.a	$1$	$2$	$2$	$6.005$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+2\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
752.2.a.f	$752$	$2$	752.a	1.a	$1$	$2$	$2$	$6.005$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+(4-\beta )q^{7}+\cdots\)
752.2.a.g	$752$	$2$	752.a	1.a	$1$	$4$	$4$	$6.005$	4.4.13448.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
752.2.a.h	$752$	$2$	752.a	1.a	$1$	$4$	$4$	$6.005$	4.4.1957.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
752.2.a.i	$752$	$2$	752.a	1.a	$1$	$4$	$4$	$6.005$	4.4.7625.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(3\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(752))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(752)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 2}\)