Space of modular forms of level 1232, weight 3, and Character 1232.m

• Label: 1232.3.m
• Level: $1232$
• Weight: $3$
• Character orbit: 1232.m
• Rep. character: $\chi_{1232}(1231,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1232.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 308 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(107\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1232, [\chi])\).

	Total	New	Old
Modular forms	396	96	300
Cusp forms	372	96	276
Eisenstein series	24	0	24

Trace form

\( 96 q + 288 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1232, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1232.3.m.a	$1232$	$3$	1232.m	308.g	$2$	$4$	$4$	$33.570$	\(\Q(\sqrt{7}, \sqrt{11})\)	\(\Q(\sqrt{-77}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}-7q^{7}+(9+\beta _{2})q^{9}-11q^{11}+\cdots\)
1232.3.m.b	$1232$	$3$	1232.m	308.g	$2$	$4$	$4$	$33.570$	\(\Q(\sqrt{7}, \sqrt{11})\)	\(\Q(\sqrt{-77}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(28\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+7q^{7}+(9+\beta _{2})q^{9}+11q^{11}+\cdots\)
1232.3.m.c	$1232$	$3$	1232.m	308.g	$2$	$8$	$8$	$33.570$	8.0.\(\cdots\).137	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{2}-2\beta _{5})q^{7}+\cdots\)
1232.3.m.d	$1232$	$3$	1232.m	308.g	$2$	$16$	$16$	$33.570$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{3}-\beta _{8}q^{5}+(\beta _{2}+\beta _{11})q^{7}+\cdots\)
1232.3.m.e	$1232$	$3$	1232.m	308.g	$2$	$16$	$16$	$33.570$	16.0.\(\cdots\).14	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{2})q^{3}+(\beta _{8}+\beta _{12})q^{5}+\cdots\)
1232.3.m.f	$1232$	$3$	1232.m	308.g	$2$	$48$	$48$	$33.570$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1232, [\chi]) \cong \)