Space of modular forms of level 220, weight 6, and Character 220.b

• Label: 220.6.b
• Level: $220$
• Weight: $6$
• Character orbit: 220.b
• Rep. character: $\chi_{220}(89,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	220.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$216$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(220, [\chi])$.

	Total	New	Old
Modular forms	186	26	160
Cusp forms	174	26	148
Eisenstein series	12	0	12

Trace form

26 * q - 31 * q^5 - 2748 * q^9 + 242 * q^11 + 1631 * q^15 - 2440 * q^19 + 2908 * q^21 + 1913 * q^25 - 19904 * q^29 - 4306 * q^31 + 23438 * q^35 + 2784 * q^39 - 1648 * q^41 + 33380 * q^45 - 60234 * q^49 - 72756 * q^51 - 6897 * q^55 + 88614 * q^59 + 39360 * q^61 - 131368 * q^65 + 32738 * q^69 - 116042 * q^71 - 154303 * q^75 + 104284 * q^79 + 129582 * q^81 - 88818 * q^85 - 51434 * q^89 + 104000 * q^91 + 25908 * q^95 + 56144 * q^99

Decomposition of $S_{6}^{\mathrm{new}}(220, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
220.6.b.a	$220$	$6$	220.b	5.b	$2$	$12$	$12$	$35.284$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			220.6.b.a	$2$	$0$	$0$	$0$	$13$	$0$	$2^{10}\cdot 3^{2}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+\beta _{8}q^{7}+(-134+\cdots)q^{9}+\cdots$
220.6.b.b	$220$	$6$	220.b	5.b	$2$	$14$	$14$	$35.284$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓		220.6.b.b	$2$	$0$	$0$	$0$	$-44$	$0$	$2^{15}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-3+\beta _{4})q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$

Decomposition of $S_{6}^{\mathrm{old}}(220, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(220, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(5, [\chi])$$^{\oplus 6}$$\oplus$$S_{6}^{\mathrm{new}}(10, [\chi])$$^{\oplus 4}$$\oplus$$S_{6}^{\mathrm{new}}(20, [\chi])$$^{\oplus 2}$$\oplus$$S_{6}^{\mathrm{new}}(55, [\chi])$$^{\oplus 3}$$\oplus$$S_{6}^{\mathrm{new}}(110, [\chi])$$^{\oplus 2}$