Space of modular forms of level 483, weight 2, and Character 483.h

• Label: 483.2.h
• Level: $483$
• Weight: $2$
• Character orbit: 483.h
• Rep. character: $\chi_{483}(160,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $128$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(128\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(483, [\chi])\).

	Total	New	Old
Modular forms	68	32	36
Cusp forms	60	32	28
Eisenstein series	8	0	8

Trace form

\( 32 q - 4 q^{2} + 36 q^{4} - 12 q^{8} - 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(483, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
483.2.h.a	$483$	$2$	483.h	161.c	$2$	$8$	$8$	$3.857$	8.0.342102016.5	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots\)
483.2.h.b	$483$	$2$	483.h	161.c	$2$	$12$	$12$	$3.857$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
483.2.h.c	$483$	$2$	483.h	161.c	$2$	$12$	$12$	$3.857$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{9}q^{3}+(3+\beta _{7})q^{4}-\beta _{5}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)