Space of modular forms of level 880, weight 2, and Character 880.bf

• Label: 880.2.bf
• Level: $880$
• Weight: $2$
• Character orbit: 880.bf
• Rep. character: $\chi_{880}(287,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $8$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bf (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(880, [\chi])\).

	Total	New	Old
Modular forms	312	60	252
Cusp forms	264	60	204
Eisenstein series	48	0	48

Trace form

\( 60 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(880, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.2.bf.a	$880$	$2$	880.bf	20.e	$4$	$2$	$1$	$7.027$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2i)q^{3}+(-2+i)q^{5}+5iq^{9}+\cdots\)
880.2.bf.b	$880$	$2$	880.bf	20.e	$4$	$2$	$1$	$7.027$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}+(-3+3i)q^{7}-3iq^{9}+\cdots\)
880.2.bf.c	$880$	$2$	880.bf	20.e	$4$	$2$	$1$	$7.027$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}+(3-3i)q^{7}-3iq^{9}+\cdots\)
880.2.bf.d	$880$	$2$	880.bf	20.e	$4$	$2$	$1$	$7.027$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2+2i)q^{3}+(-2+i)q^{5}+5iq^{9}+\cdots\)
880.2.bf.e	$880$	$2$	880.bf	20.e	$4$	$6$	$3$	$7.027$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(-2\)	\(6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
880.2.bf.f	$880$	$2$	880.bf	20.e	$4$	$6$	$3$	$7.027$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(2\)	\(6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
880.2.bf.g	$880$	$2$	880.bf	20.e	$4$	$20$	$10$	$7.027$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{3}-\beta _{14}q^{5}-\beta _{19}q^{7}+(\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
880.2.bf.h	$880$	$2$	880.bf	20.e	$4$	$20$	$10$	$7.027$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}-\beta _{14}q^{5}+\beta _{19}q^{7}+(\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)