Space of modular forms of level 220, weight 4, and Character 220.b

• Label: 220.4.b
• Level: $220$
• Weight: $4$
• Character orbit: 220.b
• Rep. character: $\chi_{220}(89,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	220.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(220, [\chi])\).

	Total	New	Old
Modular forms	114	14	100
Cusp forms	102	14	88
Eisenstein series	12	0	12

Trace form

14 * q - 16 * q^5 - 30 * q^9 - 22 * q^11 - 208 * q^15 + 144 * q^19 - 248 * q^21 + 176 * q^25 - 164 * q^29 + 92 * q^31 - 40 * q^35 - 1008 * q^39 - 748 * q^41 + 458 * q^45 - 1394 * q^49 + 1680 * q^51 + 198 * q^55 + 192 * q^59 + 180 * q^61 + 368 * q^65 + 1268 * q^69 - 1628 * q^71 - 496 * q^75 - 1056 * q^79 - 786 * q^81 + 788 * q^85 + 3460 * q^89 + 2360 * q^91 + 3168 * q^95 + 374 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(220, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
220.4.b.a	$220$	$4$	220.b	5.b	$2$	$2$	$2$	$12.980$	\(\Q(\sqrt{-19}) \)	None		✓			220.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\beta )q^{3}+(-5+5\beta )q^{5}+(2-4\beta )q^{7}+\cdots\)
220.4.b.b	$220$	$4$	220.b	5.b	$2$	$6$	$6$	$12.980$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓			220.4.b.b	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{4})q^{5}+\beta _{3}q^{7}+\cdots\)
220.4.b.c	$220$	$4$	220.b	5.b	$2$	$6$	$6$	$12.980$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓			220.4.b.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(3\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(220, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)