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

• Label: 440.2.bi
• Level: $440$
• Weight: $2$
• Character orbit: 440.bi
• Rep. character: $\chi_{440}(141,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $192$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.bi (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	304	192	112
Cusp forms	272	192	80
Eisenstein series	32	0	32

Trace form

\( 192 q + 4 q^{2} - 4 q^{4} + 8 q^{7} + 4 q^{8} + 48 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
440.2.bi.a	$440$	$2$	440.bi	88.o	$10$	$8$	$2$	$3.513$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
440.2.bi.b	$440$	$2$	440.bi	88.o	$10$	$8$	$2$	$3.513$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
440.2.bi.c	$440$	$2$	440.bi	88.o	$10$	$176$	$44$	$3.513$		None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(18\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)