Space of modular forms of level 1472, weight 2, and Character 1472.h

• Label: 1472.2.h
• Level: $1472$
• Weight: $2$
• Character orbit: 1472.h
• Rep. character: $\chi_{1472}(735,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1472, [\chi])\).

	Total	New	Old
Modular forms	204	48	156
Cusp forms	180	48	132
Eisenstein series	24	0	24

Trace form

\( 48 q + 48 q^{9} + 48 q^{25} + 48 q^{49} + 144 q^{81}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1472, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1472.2.h.a	$1472$	$2$	1472.h	184.h	$2$	$8$	$8$	$11.754$	8.0.\(\cdots\).3	\(\Q(\sqrt{-46}) \)		✓			1472.2.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{5}-3q^{9}-\beta _{4}q^{11}+\beta _{7}q^{19}+\cdots\)
1472.2.h.b	$1472$	$2$	1472.h	184.h	$2$	$8$	$8$	$11.754$	8.0.157351936.1	None		✓			1472.2.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{3}q^{5}+\beta _{7}q^{7}+4q^{9}-\beta _{5}q^{11}+\cdots\)
1472.2.h.c	$1472$	$2$	1472.h	184.h	$2$	$32$	$32$	$11.754$		None		✓	✓		1472.2.h.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1472, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1472, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(736, [\chi])\)\(^{\oplus 2}\)