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

• Label: 880.3.i
• Level: $880$
• Weight: $3$
• Character orbit: 880.i
• Rep. character: $\chi_{880}(769,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $9$
• Sturm bound: $432$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	880.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(432\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	300	74	226
Cusp forms	276	70	206
Eisenstein series	24	4	20

Trace form

\( 70 q - 2 q^{5} - 202 q^{9} + 2 q^{11} + 8 q^{15} - 18 q^{25} + 4 q^{31} - 34 q^{45} + 194 q^{49} + 114 q^{55} + 36 q^{59} + 32 q^{69} - 220 q^{71} + 272 q^{75} + 518 q^{81} - 116 q^{89} + 104 q^{91} + 274 q^{99}+O(q^{100}) \)

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.i.a	$880$	$3$	880.i	55.d	$2$	$2$	$2$	$23.978$	\(\Q(\sqrt{11}) \)	\(\Q(\sqrt{-55}) \)	✓				55.3.d.c	$4$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-5q^{5}+\beta q^{7}+9q^{9}-11q^{11}+\beta q^{13}+\cdots\)
880.3.i.b	$880$	$3$	880.i	55.d	$2$	$2$	$2$	$23.978$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)					55.3.d.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(1-2\beta )q^{3}+(-1+3\beta )q^{5}-2q^{9}+\cdots\)
880.3.i.c	$880$	$3$	880.i	55.d	$2$	$2$	$2$	$23.978$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-55}) \)	✓				55.3.d.b	$4$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+5q^{5}+\beta q^{7}+9q^{9}+11q^{11}-5\beta q^{13}+\cdots\)
880.3.i.d	$880$	$3$	880.i	55.d	$2$	$4$	$4$	$23.978$	\(\Q(\sqrt{5}, \sqrt{-21})\)	None					55.3.d.d	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2+\beta _{1})q^{5}+5\beta _{2}q^{7}+\cdots\)
880.3.i.e	$880$	$3$	880.i	55.d	$2$	$4$	$4$	$23.978$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)					220.3.e.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2^{3}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-13-2\beta _{1}-2\beta _{2}+\cdots)q^{9}+\cdots\)
880.3.i.f	$880$	$3$	880.i	55.d	$2$	$4$	$4$	$23.978$	\(\Q(\sqrt{2}, \sqrt{-13})\)	None					110.3.c.a	$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+5q^{5}+2\beta _{2}q^{7}-17q^{9}+\cdots\)
880.3.i.g	$880$	$3$	880.i	55.d	$2$	$8$	$8$	$23.978$	8.0.\(\cdots\).7	None					110.3.c.b	$4$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{5}-\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots\)
880.3.i.h	$880$	$3$	880.i	55.d	$2$	$8$	$8$	$23.978$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					220.3.e.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(\beta _{1}+\beta _{4}+\beta _{6})q^{5}+\beta _{2}q^{7}+\cdots\)
880.3.i.i	$880$	$3$	880.i	55.d	$2$	$36$	$36$	$23.978$		None			✓		440.3.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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