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

• Label: 880.2.bd
• Level: $880$
• Weight: $2$
• Character orbit: 880.bd
• Rep. character: $\chi_{880}(417,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $68$
• Newform subspaces: $9$
• Sturm bound: $288$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bd (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(288\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	312	76	236
Cusp forms	264	68	196
Eisenstein series	48	8	40

Trace form

\( 68 q + 4 q^{3} - 4 q^{5} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.2.bd.a	$880$	$2$	880.bd	55.e	$4$	$4$	$2$	$7.027$	\(\Q(\zeta_{8})\)	None					440.2.v.a	$4$	$1$	\(0\)	\(-4\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\zeta_{8})q^{3}+(-2-\zeta_{8})q^{5}+(-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
880.2.bd.b	$880$	$2$	880.bd	55.e	$4$	$4$	$2$	$7.027$	\(\Q(\zeta_{8})\)	None					110.2.f.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
880.2.bd.c	$880$	$2$	880.bd	55.e	$4$	$4$	$2$	$7.027$	\(\Q(\zeta_{8})\)	None					110.2.f.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
880.2.bd.d	$880$	$2$	880.bd	55.e	$4$	$4$	$2$	$7.027$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)					55.2.e.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
880.2.bd.e	$880$	$2$	880.bd	55.e	$4$	$4$	$2$	$7.027$	\(\Q(i, \sqrt{10})\)	None					55.2.e.a	$4$	$0$	\(0\)	\(4\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1})q^{3}+(-2+\beta _{1})q^{5}+\beta _{1}q^{9}+\cdots\)
880.2.bd.f	$880$	$2$	880.bd	55.e	$4$	$4$	$2$	$7.027$	\(\Q(i, \sqrt{11})\)	None					220.2.k.a	$4$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1})q^{3}+(-1+2\beta _{1})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bd.g	$880$	$2$	880.bd	55.e	$4$	$4$	$2$	$7.027$	\(\Q(\zeta_{8})\)	None					110.2.f.a	$4$	$0$	\(0\)	\(4\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8})q^{3}+(2-\zeta_{8})q^{5}+(2\zeta_{8}^{2}+2\zeta_{8}^{3})q^{7}+\cdots\)
880.2.bd.h	$880$	$2$	880.bd	55.e	$4$	$8$	$4$	$7.027$	8.0.303595776.1	\(\Q(\sqrt{-11}) \)					220.2.k.b	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{3}+(\beta _{2}+\beta _{6})q^{5}+(\beta _{1}-3\beta _{2}+\cdots)q^{9}+\cdots\)
880.2.bd.i	$880$	$2$	880.bd	55.e	$4$	$32$	$16$	$7.027$		None			✓		440.2.v.b	$4$	$0$	\(0\)	\(4\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)