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

• Label: 220.2.d
• Level: $220$
• Weight: $2$
• Character orbit: 220.d
• Rep. character: $\chi_{220}(131,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $72$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(72\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	40	24	16
Cusp forms	32	24	8
Eisenstein series	8	0	8

Trace form

24 * q + 4 * q^4 - 32 * q^9 + 24 * q^16 - 4 * q^20 - 24 * q^22 + 24 * q^25 - 12 * q^26 - 24 * q^33 + 48 * q^34 - 24 * q^36 - 32 * q^37 + 40 * q^42 - 4 * q^44 + 56 * q^48 + 16 * q^49 - 16 * q^53 - 48 * q^56 - 48 * q^58 - 28 * q^60 - 44 * q^64 - 36 * q^66 - 32 * q^69 - 28 * q^70 + 8 * q^77 + 48 * q^78 - 16 * q^80 + 88 * q^81 - 8 * q^82 - 20 * q^86 - 8 * q^88 + 8 * q^89 + 48 * q^92 + 32 * q^93 + 16 * 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.d.a	$220$	$2$	220.d	44.c	$2$	$2$	$2$	$1.757$	\(\Q(\sqrt{-2}) \)	None		✓			220.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+\beta q^{3}-2q^{4}-q^{5}-2q^{6}+\cdots\)
220.2.d.b	$220$	$2$	220.d	44.c	$2$	$2$	$2$	$1.757$	\(\Q(\sqrt{-2}) \)	None		✓			220.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-2q^{4}-q^{5}+2q^{6}+\cdots\)
220.2.d.c	$220$	$2$	220.d	44.c	$2$	$8$	$8$	$1.757$	8.0.\(\cdots\).7	None		✓			220.2.d.c	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
220.2.d.d	$220$	$2$	220.d	44.c	$2$	$12$	$12$	$1.757$	12.0.\(\cdots\).1	None		✓	✓		220.2.d.d	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}-\beta _{4}q^{3}+\beta _{10}q^{4}+q^{5}+(-\beta _{3}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)