Space of modular forms of level 880, weight 3, and Character 880.j

• Label: 880.3.j
• Level: $880$
• Weight: $3$
• Character orbit: 880.j
• Rep. character: $\chi_{880}(241,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	880.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(880, [\chi])\).

	Total	New	Old
Modular forms	300	48	252
Cusp forms	276	48	228
Eisenstein series	24	0	24

Trace form

48 * q + 160 * q^9 - 16 * q^11 + 64 * q^23 + 240 * q^25 + 32 * q^33 - 96 * q^37 + 96 * q^47 - 384 * q^49 + 192 * q^53 + 224 * q^59 + 160 * q^67 - 64 * q^69 + 352 * q^71 + 288 * q^77 + 464 * q^81 - 272 * q^89 - 96 * q^91 + 320 * q^93 - 288 * q^97 - 400 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(880, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.3.j.a	$880$	$3$	880.j	11.b	$2$	$8$	$8$	$23.978$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					55.3.c.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{4})q^{3}+\beta _{6}q^{5}-\beta _{7}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
880.3.j.b	$880$	$3$	880.j	11.b	$2$	$8$	$8$	$23.978$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					220.3.f.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{5}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2}-\beta _{3})q^{3}+\beta _{3}q^{5}-\beta _{5}q^{7}+\cdots\)
880.3.j.c	$880$	$3$	880.j	11.b	$2$	$8$	$8$	$23.978$	8.0.4956160000.2	None					110.3.d.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1}+\beta _{3})q^{3}-\beta _{1}q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots\)
880.3.j.d	$880$	$3$	880.j	11.b	$2$	$24$	$24$	$23.978$		None			✓		440.3.j.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)