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

• Label: 483.2.q
• Level: $483$
• Weight: $2$
• Character orbit: 483.q
• Rep. character: $\chi_{483}(64,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $240$
• Newform subspaces: $6$
• Sturm bound: $128$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(128\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	680	240	440
Cusp forms	600	240	360
Eisenstein series	80	0	80

Trace form

240 * q + 4 * q^2 - 12 * q^4 + 8 * q^6 + 4 * q^7 + 12 * q^8 - 24 * q^9 + 8 * q^10 + 16 * q^11 + 16 * q^13 + 4 * q^14 + 16 * q^15 - 32 * q^16 - 28 * q^17 + 4 * q^18 - 12 * q^19 + 40 * q^20 + 4 * q^21 - 24 * q^22 - 20 * q^23 + 24 * q^24 - 44 * q^25 - 32 * q^26 + 12 * q^28 - 12 * q^29 + 16 * q^30 + 12 * q^31 + 24 * q^32 + 8 * q^33 - 12 * q^34 + 8 * q^35 - 34 * q^36 - 4 * q^37 + 32 * q^38 - 72 * q^39 + 20 * q^40 - 64 * q^41 + 4 * q^42 + 4 * q^43 - 74 * q^44 - 112 * q^46 - 104 * q^47 - 144 * q^48 - 24 * q^49 - 70 * q^50 - 4 * q^51 + 96 * q^52 - 40 * q^53 - 36 * q^54 - 60 * q^55 + 36 * q^56 - 28 * q^57 + 58 * q^58 + 56 * q^59 + 12 * q^60 + 64 * q^61 + 120 * q^62 + 4 * q^63 - 44 * q^64 + 24 * q^65 + 64 * q^66 + 36 * q^67 + 112 * q^68 + 24 * q^69 + 8 * q^70 + 88 * q^71 + 12 * q^72 + 20 * q^73 + 122 * q^74 + 16 * q^75 - 148 * q^76 - 72 * q^77 + 8 * q^78 - 16 * q^79 + 224 * q^80 - 24 * q^81 - 104 * q^82 - 56 * q^83 + 12 * q^84 + 44 * q^85 - 232 * q^86 + 40 * q^87 + 162 * q^88 - 192 * q^89 + 8 * q^90 - 152 * q^91 + 168 * q^92 + 56 * q^93 + 136 * q^94 - 16 * q^95 + 8 * q^96 - 176 * q^97 - 18 * q^98 + 16 * q^99

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.q.a	$483$	$2$	483.q	23.c	$11$	$10$	$1$	$3.857$	\(\Q(\zeta_{22})\)	None		✓			483.2.q.a	$2$	$0$	\(4\)	\(-1\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
483.2.q.b	$483$	$2$	483.q	23.c	$11$	$10$	$1$	$3.857$	\(\Q(\zeta_{22})\)	None		✓			483.2.q.b	$2$	$0$	\(5\)	\(-1\)	\(-5\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\)
483.2.q.c	$483$	$2$	483.q	23.c	$11$	$20$	$2$	$3.857$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			483.2.q.c	$2$	$0$	\(-4\)	\(-2\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{12}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots\)
483.2.q.d	$483$	$2$	483.q	23.c	$11$	$60$	$6$	$3.857$		None		✓			483.2.q.d	$2$	$0$	\(-1\)	\(6\)	\(-13\)	\(-6\)		$\mathrm{SU}(2)[C_{11}]$
483.2.q.e	$483$	$2$	483.q	23.c	$11$	$60$	$6$	$3.857$		None		✓			483.2.q.e	$2$	$0$	\(-1\)	\(6\)	\(5\)	\(6\)		$\mathrm{SU}(2)[C_{11}]$
483.2.q.f	$483$	$2$	483.q	23.c	$11$	$80$	$8$	$3.857$		None		✓	✓		483.2.q.f	$2$	$0$	\(1\)	\(-8\)	\(13\)	\(8\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(483, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)