Space of modular forms of level 483, weight 4, and trivial character

• Label: 483.4.a
• Level: $483$
• Weight: $4$
• Character orbit: 483.a
• Rep. character: $\chi_{483}(1,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $9$
• Sturm bound: $256$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(256\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(483))\).

	Total	New	Old
Modular forms	196	64	132
Cusp forms	188	64	124
Eisenstein series	8	0	8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(7\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(9\)
\(+\)	\(+\)	\(-\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(-\)	$+$	\(9\)
\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(-\)	\(+\)	\(-\)	$+$	\(9\)
\(-\)	\(-\)	\(+\)	$+$	\(9\)
\(-\)	\(-\)	\(-\)	$-$	\(7\)
Plus space			\(+\)	\(36\)
Minus space			\(-\)	\(28\)

Trace form

\( 64 q + 8 q^{2} + 240 q^{4} + 32 q^{5} + 96 q^{8} + 576 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(483))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	23
483.4.a.a	$483$	$4$	483.a	1.a	$1$	$3$	$3$	$28.498$	3.3.3877.1	None	✓	$1$	$1$	\(-4\)	\(9\)	\(2\)	\(-21\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+3q^{3}+(1+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.4.a.b	$483$	$4$	483.a	1.a	$1$	$4$	$4$	$28.498$	4.4.8184789.1	None	✓	$1$	$1$	\(2\)	\(12\)	\(-23\)	\(-28\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+3q^{3}+(3+\beta _{1})q^{4}+(-6+\cdots)q^{5}+\cdots\)
483.4.a.c	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(21\)	\(-41\)	\(49\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
483.4.a.d	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-21\)	\(-11\)	\(-49\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{4}+\beta _{5})q^{4}+\cdots\)
483.4.a.e	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(2\)	\(-21\)	\(-11\)	\(49\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
483.4.a.f	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-27\)	\(29\)	\(63\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(3+\beta _{7}+\cdots)q^{5}+\cdots\)
483.4.a.g	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(-27\)	\(9\)	\(-63\)		$+$	$+$	$+$	$+$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.4.a.h	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(27\)	\(39\)	\(-63\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(4+\beta _{4}+\cdots)q^{5}+\cdots\)
483.4.a.i	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(27\)	\(39\)	\(63\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(4-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(483))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(483)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)