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		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(29\)	\(9\)	\(20\)		\(28\)	\(9\)	\(19\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(21\)	\(7\)	\(14\)		\(20\)	\(7\)	\(13\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(22\)	\(7\)	\(15\)		\(21\)	\(7\)	\(14\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(26\)	\(9\)	\(17\)		\(25\)	\(9\)	\(16\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(24\)	\(7\)	\(17\)		\(23\)	\(7\)	\(16\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(24\)	\(9\)	\(15\)		\(23\)	\(9\)	\(14\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(23\)	\(9\)	\(14\)		\(22\)	\(9\)	\(13\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(27\)	\(7\)	\(20\)		\(26\)	\(7\)	\(19\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(102\)	\(36\)	\(66\)		\(98\)	\(36\)	\(62\)		\(4\)	\(0\)	\(4\)
Minus space			\(-\)		\(94\)	\(28\)	\(66\)		\(90\)	\(28\)	\(62\)		\(4\)	\(0\)	\(4\)

Trace form

64 * q + 8 * q^2 + 240 * q^4 + 32 * q^5 + 96 * q^8 + 576 * q^9 - 64 * q^10 - 48 * q^12 + 288 * q^13 + 976 * q^16 - 176 * q^17 + 72 * q^18 + 416 * q^20 + 432 * q^22 + 1864 * q^25 - 144 * q^26 + 592 * q^29 + 816 * q^30 - 240 * q^31 - 344 * q^32 - 192 * q^33 - 696 * q^34 + 2160 * q^36 - 64 * q^37 - 2592 * q^38 - 624 * q^39 - 632 * q^40 + 1792 * q^41 - 1088 * q^43 - 864 * q^44 + 288 * q^45 - 368 * q^46 - 864 * q^47 - 384 * q^48 + 3136 * q^49 + 800 * q^50 + 240 * q^51 + 5752 * q^52 + 288 * q^53 - 1984 * q^55 - 768 * q^57 - 80 * q^58 - 1696 * q^59 - 1224 * q^60 + 2192 * q^61 + 1656 * q^62 + 2520 * q^64 - 640 * q^65 + 2544 * q^66 - 1712 * q^67 + 2104 * q^68 - 1064 * q^70 - 944 * q^71 + 864 * q^72 - 528 * q^73 + 5256 * q^74 + 2304 * q^75 - 3000 * q^76 - 448 * q^77 - 3312 * q^78 - 1888 * q^79 + 8952 * q^80 + 5184 * q^81 + 1624 * q^82 - 96 * q^83 + 1488 * q^85 - 2976 * q^86 + 288 * q^87 + 6776 * q^88 + 128 * q^89 - 576 * q^90 - 744 * q^93 + 3256 * q^94 + 2784 * q^95 - 600 * q^96 + 7104 * q^97 + 392 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	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	✓	✓			483.4.a.a	$1$	$1$	\(-4\)	\(9\)	\(2\)	\(-21\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+3q^{3}+(1+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.4.a.b	$483$	$4$	483.a	1.a	$1$	$4$	$4$	$28.498$	4.4.8184789.1	None	✓	✓	✓		483.4.a.b	$1$	$1$	\(2\)	\(12\)	\(-23\)	\(-28\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+3q^{3}+(3+\beta _{1})q^{4}+(-6+\cdots)q^{5}+\cdots\)
483.4.a.c	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	483.4.a.c	$1$	$1$	\(-6\)	\(21\)	\(-41\)	\(49\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
483.4.a.d	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	483.4.a.d	$1$	$1$	\(-2\)	\(-21\)	\(-11\)	\(-49\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{4}+\beta _{5})q^{4}+\cdots\)
483.4.a.e	$483$	$4$	483.a	1.a	$1$	$7$	$7$	$28.498$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	483.4.a.e	$1$	$1$	\(2\)	\(-21\)	\(-11\)	\(49\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
483.4.a.f	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	483.4.a.f	$1$	$0$	\(0\)	\(-27\)	\(29\)	\(63\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(3+\beta _{7}+\cdots)q^{5}+\cdots\)
483.4.a.g	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	483.4.a.g	$1$	$0$	\(4\)	\(-27\)	\(9\)	\(-63\)		$+$	$+$	$+$	$+$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.4.a.h	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	483.4.a.h	$1$	$0$	\(4\)	\(27\)	\(39\)	\(-63\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(4+\beta _{4}+\cdots)q^{5}+\cdots\)
483.4.a.i	$483$	$4$	483.a	1.a	$1$	$9$	$9$	$28.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	483.4.a.i	$1$	$0$	\(8\)	\(27\)	\(39\)	\(63\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(4-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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

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