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

• Label: 483.2.i
• Level: $483$
• Weight: $2$
• Character orbit: 483.i
• Rep. character: $\chi_{483}(277,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $60$
• Newform subspaces: $8$
• Sturm bound: $128$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(128\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	136	60	76
Cusp forms	120	60	60
Eisenstein series	16	0	16

Trace form

60 * q + 2 * q^3 - 32 * q^4 - 8 * q^6 + 6 * q^7 + 24 * q^8 - 30 * q^9 - 16 * q^10 + 4 * q^12 - 4 * q^13 - 12 * q^14 + 8 * q^15 - 52 * q^16 - 8 * q^17 - 6 * q^19 - 16 * q^20 - 8 * q^21 + 48 * q^22 - 46 * q^25 + 32 * q^26 - 4 * q^27 + 28 * q^28 + 24 * q^29 + 22 * q^31 - 24 * q^32 - 12 * q^33 - 16 * q^34 + 4 * q^35 + 64 * q^36 - 10 * q^37 - 20 * q^38 + 2 * q^39 - 36 * q^40 + 8 * q^41 + 16 * q^42 - 12 * q^43 - 16 * q^44 - 8 * q^47 - 16 * q^48 + 50 * q^49 - 40 * q^50 + 4 * q^54 - 48 * q^55 - 8 * q^56 + 12 * q^57 + 24 * q^58 - 20 * q^59 + 12 * q^60 - 16 * q^61 + 24 * q^62 - 6 * q^63 + 200 * q^64 + 36 * q^65 - 24 * q^66 - 10 * q^67 - 12 * q^68 - 16 * q^69 + 16 * q^70 + 8 * q^71 - 12 * q^72 + 18 * q^73 - 12 * q^74 + 14 * q^75 + 24 * q^76 + 8 * q^77 - 8 * q^78 - 10 * q^79 + 92 * q^80 - 30 * q^81 + 24 * q^82 + 56 * q^83 + 4 * q^84 - 72 * q^85 - 44 * q^86 + 20 * q^87 - 80 * q^88 + 32 * q^90 - 46 * q^91 - 6 * q^93 - 20 * q^94 - 24 * q^95 + 4 * q^96 + 40 * q^97 - 40 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
483.2.i.a	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	\(\Q(\sqrt{-3}) \)	None		✓			483.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
483.2.i.b	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	\(\Q(\sqrt{-3}) \)	None		✓			483.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
483.2.i.c	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	\(\Q(\sqrt{-3}) \)	None		✓			483.2.i.c	$2$	$0$	\(1\)	\(-1\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.d	$483$	$2$	483.i	7.c	$3$	$2$	$1$	$3.857$	\(\Q(\sqrt{-3}) \)	None		✓			483.2.i.d	$2$	$0$	\(1\)	\(-1\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.e	$483$	$2$	483.i	7.c	$3$	$4$	$2$	$3.857$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓			483.2.i.e	$2$	$0$	\(1\)	\(-2\)	\(1\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
483.2.i.f	$483$	$2$	483.i	7.c	$3$	$12$	$6$	$3.857$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			483.2.i.f	$2$	$0$	\(1\)	\(6\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{5})q^{2}+\beta _{7}q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
483.2.i.g	$483$	$2$	483.i	7.c	$3$	$16$	$8$	$3.857$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			483.2.i.g	$2$	$0$	\(-1\)	\(-8\)	\(-5\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
483.2.i.h	$483$	$2$	483.i	7.c	$3$	$20$	$10$	$3.857$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		483.2.i.h	$2$	$0$	\(-3\)	\(10\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{8}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(483, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)