Space of modular forms of level 952, weight 2, and Character 952.b

• Label: 952.2.b
• Level: $952$
• Weight: $2$
• Character orbit: 952.b
• Rep. character: $\chi_{952}(477,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $7$
• Sturm bound: $288$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(952, [\chi])\).

	Total	New	Old
Modular forms	148	96	52
Cusp forms	140	96	44
Eisenstein series	8	0	8

Trace form

\( 96 q + 2 q^{2} - 2 q^{4} - 12 q^{6} + 4 q^{7} + 14 q^{8} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(952, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
952.2.b.a	$952$	$2$	952.b	8.b	$2$	$2$	$2$	$7.602$	\(\Q(\sqrt{-2}) \)	None		✓			952.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+\beta q^{3}-2q^{4}-\beta q^{5}-2q^{6}+\cdots\)
952.2.b.b	$952$	$2$	952.b	8.b	$2$	$2$	$2$	$7.602$	\(\Q(\sqrt{-2}) \)	None		✓			952.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}-q^{7}-2\beta q^{8}+3q^{9}+\cdots\)
952.2.b.c	$952$	$2$	952.b	8.b	$2$	$2$	$2$	$7.602$	\(\Q(\sqrt{-2}) \)	None		✓			952.2.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+2\beta q^{3}-2q^{4}-2\beta q^{5}+4q^{6}+\cdots\)
952.2.b.d	$952$	$2$	952.b	8.b	$2$	$16$	$16$	$7.602$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			952.2.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(1-\beta _{6})q^{4}+\beta _{11}q^{5}+\cdots\)
952.2.b.e	$952$	$2$	952.b	8.b	$2$	$16$	$16$	$7.602$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			952.2.b.e	$2$	$0$	\(1\)	\(0\)	\(0\)	\(-16\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{8}q^{3}-\beta _{4}q^{4}+\beta _{12}q^{5}+\cdots\)
952.2.b.f	$952$	$2$	952.b	8.b	$2$	$28$	$28$	$7.602$		None		✓			952.2.b.f	$2$	$0$	\(1\)	\(0\)	\(0\)	\(-28\)		$\mathrm{SU}(2)[C_{2}]$
952.2.b.g	$952$	$2$	952.b	8.b	$2$	$30$	$30$	$7.602$		None		✓	✓		952.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(30\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(952, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(952, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)