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

• Label: 440.2.b
• Level: $440$
• Weight: $2$
• Character orbit: 440.b
• Rep. character: $\chi_{440}(89,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	80	14	66
Cusp forms	64	14	50
Eisenstein series	16	0	16

Trace form

14 * q + 4 * q^5 - 14 * q^9 + 6 * q^11 - 14 * q^15 - 8 * q^21 - 8 * q^25 - 4 * q^29 + 4 * q^35 + 16 * q^39 + 20 * q^41 - 14 * q^45 - 18 * q^49 - 24 * q^51 - 20 * q^59 + 52 * q^61 - 32 * q^65 + 12 * q^69 + 8 * q^71 + 50 * q^75 + 40 * q^79 + 46 * q^81 - 20 * q^85 + 20 * q^89 - 40 * q^91 + 24 * q^95 - 18 * 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.b.a	$440$	$2$	440.b	5.b	$2$	$2$	$2$	$3.513$	\(\Q(\sqrt{-1}) \)	None		✓			440.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+(\beta-1)q^{5}+\beta q^{7}-q^{9}+\cdots\)
440.2.b.b	$440$	$2$	440.b	5.b	$2$	$2$	$2$	$3.513$	\(\Q(\sqrt{-1}) \)	None		✓			440.2.b.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+(-\beta+1)q^{5}-2\beta q^{7}-q^{9}+\cdots\)
440.2.b.c	$440$	$2$	440.b	5.b	$2$	$2$	$2$	$3.513$	\(\Q(\sqrt{-1}) \)	None		✓			440.2.b.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i+2)q^{5}+i q^{7}+2 q^{9}+\cdots\)
440.2.b.d	$440$	$2$	440.b	5.b	$2$	$8$	$8$	$3.513$	8.0.\(\cdots\).2	None		✓	✓		440.2.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(440, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)