Space of modular forms of level 495, weight 3, and Character 495.j

• Label: 495.3.j
• Level: $495$
• Weight: $3$
• Character orbit: 495.j
• Rep. character: $\chi_{495}(298,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $100$
• Newform subspaces: $3$
• Sturm bound: $216$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(216\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(495, [\chi])\).

	Total	New	Old
Modular forms	304	100	204
Cusp forms	272	100	172
Eisenstein series	32	0	32

Trace form

100 * q - 4 * q^2 - 8 * q^5 + 12 * q^8 + 12 * q^10 - 28 * q^13 - 512 * q^16 - 48 * q^17 - 104 * q^20 + 70 * q^23 + 90 * q^25 + 96 * q^26 + 140 * q^28 - 8 * q^31 - 56 * q^32 - 132 * q^35 - 78 * q^37 - 320 * q^38 + 80 * q^40 - 152 * q^41 - 24 * q^43 + 264 * q^46 + 228 * q^47 + 368 * q^50 + 268 * q^52 + 188 * q^53 + 66 * q^55 - 360 * q^56 + 296 * q^58 + 168 * q^61 + 36 * q^62 - 272 * q^65 - 178 * q^67 - 156 * q^68 - 688 * q^70 - 84 * q^71 - 324 * q^73 - 312 * q^76 - 32 * q^80 - 688 * q^82 - 40 * q^83 - 212 * q^85 + 592 * q^86 + 264 * q^88 + 384 * q^91 + 696 * q^92 + 28 * q^95 + 562 * q^97 - 172 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(495, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.3.j.a	$495$	$3$	495.j	5.c	$4$	$20$	$10$	$13.488$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					55.3.f.a	$2$	$0$	\(4\)	\(0\)	\(8\)	\(0\)	$2^{8}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}+(-2\beta _{8}-\beta _{16})q^{4}+\beta _{15}q^{5}+\cdots\)
495.3.j.b	$495$	$3$	495.j	5.c	$4$	$40$	$20$	$13.488$		None					165.3.i.a	$2$	$0$	\(-8\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
495.3.j.c	$495$	$3$	495.j	5.c	$4$	$40$	$20$	$13.488$		None		✓			495.3.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(495, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)