Space of modular forms of level 483, weight 6, and trivial character

• Label: 483.6.a
• Level: $483$
• Weight: $6$
• Character orbit: 483.a
• Rep. character: $\chi_{483}(1,\cdot)$
• Character field: $\Q$
• Dimension: $112$
• Newform subspaces: $9$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(483))\).

	Total	New	Old
Modular forms	324	112	212
Cusp forms	316	112	204
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
\(+\)	\(+\)	\(+\)	$+$	\(13\)
\(+\)	\(+\)	\(-\)	$-$	\(15\)
\(+\)	\(-\)	\(+\)	$-$	\(15\)
\(+\)	\(-\)	\(-\)	$+$	\(13\)
\(-\)	\(+\)	\(+\)	$-$	\(15\)
\(-\)	\(+\)	\(-\)	$+$	\(13\)
\(-\)	\(-\)	\(+\)	$+$	\(13\)
\(-\)	\(-\)	\(-\)	$-$	\(15\)
Plus space			\(+\)	\(52\)
Minus space			\(-\)	\(60\)

Trace form

\( 112 q - 16 q^{2} + 1856 q^{4} - 64 q^{5} - 768 q^{8} + 9072 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(483))\) 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
483.6.a.a	$483$	$6$	483.a	1.a	$1$	$1$	$1$	$77.465$	\(\Q\)	None	✓	$1$	$1$	\(-7\)	\(9\)	\(-21\)	\(-49\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-7q^{2}+9q^{3}+17q^{4}-21q^{5}-63q^{6}+\cdots\)
483.6.a.b	$483$	$6$	483.a	1.a	$1$	$12$	$12$	$77.465$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(108\)	\(-162\)	\(-588\)		$-$	$+$	$-$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+9q^{3}+(13+\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.6.a.c	$483$	$6$	483.a	1.a	$1$	$13$	$13$	$77.465$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-16\)	\(117\)	\(-183\)	\(637\)		$-$	$-$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+9q^{3}+(13+2\beta _{1}+\cdots)q^{4}+\cdots\)
483.6.a.d	$483$	$6$	483.a	1.a	$1$	$13$	$13$	$77.465$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-8\)	\(-117\)	\(-33\)	\(-637\)		$+$	$+$	$+$	$+$	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-9q^{3}+(17-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
483.6.a.e	$483$	$6$	483.a	1.a	$1$	$13$	$13$	$77.465$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-117\)	\(-133\)	\(637\)		$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-9q^{3}+(2^{4}+\beta _{2})q^{4}+(-10+\cdots)q^{5}+\cdots\)
483.6.a.f	$483$	$6$	483.a	1.a	$1$	$15$	$15$	$77.465$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(-4\)	\(-135\)	\(67\)	\(735\)		$+$	$-$	$+$	$-$	$2^{9}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-9q^{3}+(20+\beta _{2})q^{4}+(5-\beta _{1}+\cdots)q^{5}+\cdots\)
483.6.a.g	$483$	$6$	483.a	1.a	$1$	$15$	$15$	$77.465$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(-135\)	\(67\)	\(-735\)		$+$	$+$	$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-9q^{3}+(20+\beta _{2})q^{4}+(4+\beta _{6}+\cdots)q^{5}+\cdots\)
483.6.a.h	$483$	$6$	483.a	1.a	$1$	$15$	$15$	$77.465$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(135\)	\(117\)	\(-735\)		$-$	$+$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+9q^{3}+(17+\beta _{2})q^{4}+(8+\beta _{1}+\cdots)q^{5}+\cdots\)
483.6.a.i	$483$	$6$	483.a	1.a	$1$	$15$	$15$	$77.465$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(135\)	\(217\)	\(735\)		$-$	$-$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+9q^{3}+(17-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(483))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(483)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)