Space of modular forms of level 1232, weight 2, and Character 1232.e

• Label: 1232.2.e
• Level: $1232$
• Weight: $2$
• Character orbit: 1232.e
• Rep. character: $\chi_{1232}(769,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1232, [\chi])\).

	Total	New	Old
Modular forms	204	50	154
Cusp forms	180	46	134
Eisenstein series	24	4	20

Trace form

\( 46 q - 46 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1232, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1232.2.e.a	$1232$	$2$	1232.e	77.b	$2$	$2$	$2$	$9.838$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{7}+3q^{9}+(-2-\beta )q^{11}+8q^{23}+\cdots\)
1232.2.e.b	$1232$	$2$	1232.e	77.b	$2$	$4$	$4$	$9.838$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots\)
1232.2.e.c	$1232$	$2$	1232.e	77.b	$2$	$4$	$4$	$9.838$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}-2q^{9}+\cdots\)
1232.2.e.d	$1232$	$2$	1232.e	77.b	$2$	$4$	$4$	$9.838$	\(\Q(\sqrt{-2}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
1232.2.e.e	$1232$	$2$	1232.e	77.b	$2$	$8$	$8$	$9.838$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{6}q^{5}+(\beta _{1}-\beta _{3}-\beta _{7})q^{7}+\cdots\)
1232.2.e.f	$1232$	$2$	1232.e	77.b	$2$	$24$	$24$	$9.838$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1232, [\chi]) \cong \)