Space of modular forms of level 220, weight 2, and Character 220.k

• Label: 220.2.k
• Level: $220$
• Weight: $2$
• Character orbit: 220.k
• Rep. character: $\chi_{220}(153,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.k (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$55$
Character field:			$\Q(i)$
Newform subspaces:			$2$
Sturm bound:			$72$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(220, [\chi])$.

	Total	New	Old
Modular forms	84	12	72
Cusp forms	60	12	48
Eisenstein series	24	0	24

Trace form

12 * q - 2 * q^3 - 4 * q^5 - 4 * q^15 - 6 * q^23 - 14 * q^25 + 10 * q^27 - 16 * q^31 + 22 * q^33 + 34 * q^37 + 26 * q^45 - 28 * q^47 - 36 * q^53 - 22 * q^55 - 38 * q^67 - 4 * q^71 + 60 * q^75 - 44 * q^77 - 80 * q^81 + 88 * q^91 + 34 * q^93 + 54 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(220, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
220.2.k.a	$220$	$2$	220.k	55.e	$4$	$4$	$2$	$1.757$	$\Q(i, \sqrt{11})$	None		✓			220.2.k.a	$4$	$0$	$0$	$-4$	$-4$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{3}+(-1+2\beta _{1})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
220.2.k.b	$220$	$2$	220.k	55.e	$4$	$8$	$4$	$1.757$	8.0.303595776.1	$\Q(\sqrt{-11})$		✓	✓		220.2.k.b	$4$	$0$	$0$	$2$	$0$	$0$	$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{1}q^{3}+(\beta _{2}+\beta _{6})q^{5}+(\beta _{1}-3\beta _{2}+\cdots)q^{9}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(220, [\chi])$ into lower level spaces

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