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

• Label: 220.2.m
• Level: $220$
• Weight: $2$
• Character orbit: 220.m
• Rep. character: $\chi_{220}(81,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	168	16	152
Cusp forms	120	16	104
Eisenstein series	48	0	48

Trace form

16 * q + 4 * q^3 + 6 * q^9 + 10 * q^11 + 10 * q^13 + 6 * q^15 - 4 * q^17 - 14 * q^19 - 32 * q^23 - 4 * q^25 - 8 * q^27 + 2 * q^29 + 20 * q^31 - 14 * q^33 + 8 * q^35 + 20 * q^37 + 10 * q^39 + 12 * q^41 - 12 * q^43 - 24 * q^47 - 6 * q^49 - 26 * q^51 - 24 * q^53 - 20 * q^55 - 26 * q^57 - 18 * q^59 - 12 * q^61 - 50 * q^63 - 32 * q^65 + 24 * q^67 + 10 * q^69 - 48 * q^71 + 6 * q^73 - 6 * q^75 + 6 * q^77 - 6 * q^79 - 16 * q^81 + 26 * q^83 - 8 * q^85 + 108 * q^87 - 4 * q^91 + 80 * q^93 - 4 * q^97 + 40 * q^99

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.m.a	$220$	$2$	220.m	11.c	$5$	$8$	$2$	$1.757$	8.0.26265625.1	None		✓			220.2.m.a	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
220.2.m.b	$220$	$2$	220.m	11.c	$5$	$8$	$2$	$1.757$	8.0.159390625.1	None		✓			220.2.m.b	$2$	$0$	\(0\)	\(5\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{3}+\beta _{4})q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)