Space of modular forms of level 483, weight 2, and trivial character

• Label: 483.2.a
• Level: $483$
• Weight: $2$
• Character orbit: 483.a
• Rep. character: $\chi_{483}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $10$
• Sturm bound: $128$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(128\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(483))\).

	Total	New	Old
Modular forms	68	23	45
Cusp forms	61	23	38
Eisenstein series	7	0	7

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
\(+\)	\(+\)	\(+\)	\(+\)		\(4\)	\(2\)	\(2\)		\(4\)	\(2\)	\(2\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(12\)	\(4\)	\(8\)		\(11\)	\(4\)	\(7\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(11\)	\(4\)	\(7\)		\(10\)	\(4\)	\(6\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(7\)	\(2\)	\(5\)		\(6\)	\(2\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(9\)	\(4\)	\(5\)		\(8\)	\(4\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(9\)	\(2\)	\(7\)		\(8\)	\(2\)	\(6\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(10\)	\(2\)	\(8\)		\(9\)	\(2\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(6\)	\(3\)	\(3\)		\(5\)	\(3\)	\(2\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(30\)	\(8\)	\(22\)		\(27\)	\(8\)	\(19\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(38\)	\(15\)	\(23\)		\(34\)	\(15\)	\(19\)		\(4\)	\(0\)	\(4\)

Trace form

23 * q + q^2 - q^3 + 21 * q^4 + 10 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 23 * q^9 + 6 * q^10 - 12 * q^11 + 9 * q^12 + 2 * q^13 - 3 * q^14 - 6 * q^15 + 21 * q^16 + 14 * q^17 + q^18 - 20 * q^19 - 2 * q^20 - q^21 - 20 * q^22 - q^23 - 15 * q^24 + 33 * q^25 - 18 * q^26 - q^27 - 7 * q^28 + 2 * q^29 - 2 * q^30 - 24 * q^31 + 5 * q^32 - 4 * q^33 + 10 * q^34 - 6 * q^35 + 21 * q^36 - 14 * q^37 + 36 * q^38 + 2 * q^39 + 38 * q^40 + 14 * q^41 - 3 * q^42 + 4 * q^43 + 12 * q^44 + 10 * q^45 + 5 * q^46 - 24 * q^47 + q^48 + 23 * q^49 + 7 * q^50 - 10 * q^51 - 2 * q^52 - 6 * q^53 - 3 * q^54 + 16 * q^55 - 15 * q^56 - 4 * q^57 + 6 * q^58 - 20 * q^59 - 18 * q^60 + 2 * q^61 - 24 * q^62 - q^63 - 19 * q^64 + 52 * q^65 - 20 * q^66 - 20 * q^67 + 2 * q^68 - q^69 + 14 * q^70 - 16 * q^71 - 3 * q^72 + 22 * q^73 - 18 * q^74 + 17 * q^75 - 100 * q^76 + 4 * q^77 + 30 * q^78 - 48 * q^79 - 42 * q^80 + 23 * q^81 - 30 * q^82 - 12 * q^83 - 7 * q^84 - 4 * q^85 - 84 * q^86 - 6 * q^87 - 28 * q^88 + 46 * q^89 + 6 * q^90 - 14 * q^91 - 7 * q^92 - 24 * q^93 + 8 * q^94 - 24 * q^95 - 23 * q^96 - 26 * q^97 + q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(483))\) 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
483.2.a.a	$483$	$2$	483.a	1.a	$1$	$1$	$1$	$3.857$	\(\Q\)	None	✓	✓			483.2.a.a	$1$	$0$	\(2\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
483.2.a.b	$483$	$2$	483.a	1.a	$1$	$1$	$1$	$3.857$	\(\Q\)	None	✓	✓			483.2.a.b	$1$	$0$	\(2\)	\(1\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
483.2.a.c	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	483.2.a.c	$1$	$1$	\(-3\)	\(2\)	\(-5\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
483.2.a.d	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	483.2.a.d	$1$	$1$	\(-1\)	\(-2\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
483.2.a.e	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		483.2.a.e	$1$	$0$	\(-1\)	\(2\)	\(5\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(3-\beta )q^{5}+\cdots\)
483.2.a.f	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	483.2.a.f	$1$	$1$	\(-1\)	\(2\)	\(-5\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots\)
483.2.a.g	$483$	$2$	483.a	1.a	$1$	$2$	$2$	$3.857$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	483.2.a.g	$1$	$1$	\(1\)	\(-2\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
483.2.a.h	$483$	$2$	483.a	1.a	$1$	$3$	$3$	$3.857$	3.3.837.1	None	✓	✓	✓		483.2.a.h	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
483.2.a.i	$483$	$2$	483.a	1.a	$1$	$4$	$4$	$3.857$	4.4.24197.1	None	✓	✓	✓	✓	483.2.a.i	$1$	$0$	\(0\)	\(-4\)	\(5\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
483.2.a.j	$483$	$2$	483.a	1.a	$1$	$4$	$4$	$3.857$	4.4.15317.1	None	✓	✓	✓	✓	483.2.a.j	$1$	$0$	\(2\)	\(-4\)	\(5\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(483))\) into lower level spaces

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