Space of modular forms of level 440, weight 2, and Character 440.y

• Label: 440.2.y
• Level: $440$
• Weight: $2$
• Character orbit: 440.y
• Rep. character: $\chi_{440}(81,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).

	Total	New	Old
Modular forms	320	48	272
Cusp forms	256	48	208
Eisenstein series	64	0	64

Trace form

48 * q - 4 * q^3 - 4 * q^11 - 4 * q^13 + 16 * q^17 + 14 * q^19 - 16 * q^21 + 16 * q^23 - 12 * q^25 + 14 * q^27 + 12 * q^29 - 12 * q^31 - 26 * q^33 + 8 * q^35 - 8 * q^37 - 44 * q^39 - 6 * q^41 - 60 * q^43 - 40 * q^47 - 46 * q^49 - 34 * q^51 + 48 * q^53 + 16 * q^55 - 14 * q^57 + 26 * q^59 + 48 * q^61 + 48 * q^63 + 44 * q^65 - 12 * q^67 + 64 * q^69 + 68 * q^71 + 52 * q^73 + 6 * q^75 - 36 * q^77 + 36 * q^79 - 62 * q^81 + 42 * q^83 - 4 * q^85 + 40 * q^87 - 48 * q^89 - 14 * q^91 + 16 * q^93 - 50 * q^97 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
440.2.y.a	$440$	$2$	440.y	11.c	$5$	$8$	$2$	$3.513$	8.0.13140625.1	None		✓			440.2.y.a	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}-\beta _{5})q^{3}+\beta _{7}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
440.2.y.b	$440$	$2$	440.y	11.c	$5$	$12$	$3$	$3.513$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			440.2.y.b	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}+\beta _{4})q^{3}+(1-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
440.2.y.c	$440$	$2$	440.y	11.c	$5$	$12$	$3$	$3.513$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			440.2.y.c	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{3}+\beta _{8})q^{3}-\beta _{6}q^{5}+(1+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
440.2.y.d	$440$	$2$	440.y	11.c	$5$	$16$	$4$	$3.513$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		440.2.y.d	$2$	$0$	\(0\)	\(-3\)	\(-4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(440, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)