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

• Label: 1472.2.j
• Level: $1472$
• Weight: $2$
• Character orbit: 1472.j
• Rep. character: $\chi_{1472}(369,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $88$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	400	88	312
Cusp forms	368	88	280
Eisenstein series	32	0	32

Trace form

\( 88 q - 12 q^{27} - 24 q^{31} - 24 q^{35} + 32 q^{43} + 40 q^{47} - 88 q^{49} + 40 q^{51} - 20 q^{59} - 16 q^{65} + 24 q^{67} + 24 q^{75} - 88 q^{81} - 40 q^{83} - 16 q^{91} - 24 q^{93} - 16 q^{95} - 64 q^{99}+O(q^{100}) \)

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.j.a	$1472$	$2$	1472.j	16.e	$4$	$2$	$1$	$11.754$	\(\Q(\sqrt{-1}) \)	None					368.2.j.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+4 i q^{7}+i q^{9}+(-4 i-4)q^{11}+\cdots\)
1472.2.j.b	$1472$	$2$	1472.j	16.e	$4$	$4$	$2$	$11.754$	\(\Q(\zeta_{12})\)	None					368.2.j.b	$2$	$0$	\(0\)	\(6\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta_{3}-\beta_{2}+1)q^{3}+(-\beta_{2}-1)q^{5}+\cdots\)
1472.2.j.c	$1472$	$2$	1472.j	16.e	$4$	$12$	$6$	$11.754$	12.0.\(\cdots\).1	None					368.2.j.c	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
1472.2.j.d	$1472$	$2$	1472.j	16.e	$4$	$24$	$12$	$11.754$		None					368.2.j.d	$2$	$0$	\(0\)	\(4\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1472.2.j.e	$1472$	$2$	1472.j	16.e	$4$	$46$	$23$	$11.754$		None			✓		368.2.j.e	$2$	$0$	\(0\)	\(-6\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1472, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 3}\)