Space of modular forms of level 220, weight 3, and Character 220.q

• Label: 220.3.q
• Level: $220$
• Weight: $3$
• Character orbit: 220.q
• Rep. character: $\chi_{220}(29,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.q (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(220, [\chi])\).

	Total	New	Old
Modular forms	312	48	264
Cusp forms	264	48	216
Eisenstein series	48	0	48

Trace form

48 * q + 5 * q^5 + 20 * q^9 - 23 * q^15 - 7 * q^25 - 74 * q^31 + 155 * q^35 + 80 * q^39 - 20 * q^41 + 12 * q^45 + 102 * q^49 + 220 * q^51 - 69 * q^55 + 40 * q^59 - 290 * q^61 - 234 * q^69 - 406 * q^71 + 153 * q^75 - 280 * q^79 + 230 * q^81 - 465 * q^85 - 636 * q^89 + 512 * q^91 - 495 * q^95 - 382 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(220, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
220.3.q.a	$220$	$3$	220.q	55.h	$10$	$48$	$12$	$5.995$		None		✓	✓	✓	220.3.q.a	$4$	$0$	\(0\)	\(0\)	\(5\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)