Space of modular forms of level 880, weight 4, and Character 880.b

• Label: 880.4.b
• Level: $880$
• Weight: $4$
• Character orbit: 880.b
• Rep. character: $\chi_{880}(529,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $11$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	880.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(880, [\chi])\).

	Total	New	Old
Modular forms	444	90	354
Cusp forms	420	90	330
Eisenstein series	24	0	24

Trace form

90 * q - 2 * q^5 - 810 * q^9 + 66 * q^11 + 6 * q^15 - 24 * q^19 + 136 * q^21 + 22 * q^25 - 228 * q^29 - 636 * q^31 + 228 * q^35 - 236 * q^41 + 90 * q^45 - 4410 * q^49 - 744 * q^51 - 2468 * q^59 - 132 * q^61 + 1336 * q^65 + 1544 * q^69 - 1932 * q^71 + 3134 * q^75 + 4440 * q^79 + 7282 * q^81 - 632 * q^85 + 644 * q^89 + 464 * q^91 - 5592 * q^95 - 1782 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(880, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.4.b.a	$880$	$4$	880.b	5.b	$2$	$2$	$2$	$51.922$	\(\Q(\sqrt{-1}) \)	None					110.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+9 i q^{3}+(5 i-10)q^{5}-5 i q^{7}+\cdots\)
880.4.b.b	$880$	$4$	880.b	5.b	$2$	$2$	$2$	$51.922$	\(\Q(\sqrt{-19}) \)	None					220.4.b.a	$2$	$1$	\(0\)	\(0\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\beta )q^{3}-5\beta q^{5}+(2-4\beta )q^{7}+\cdots\)
880.4.b.c	$880$	$4$	880.b	5.b	$2$	$2$	$2$	$51.922$	\(\Q(\sqrt{-1}) \)	None					440.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5 i q^{3}+(11 i-2)q^{5}-13 i q^{7}+\cdots\)
880.4.b.d	$880$	$4$	880.b	5.b	$2$	$4$	$4$	$51.922$	\(\Q(i, \sqrt{89})\)	None					110.4.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(3\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+9\beta _{2}+\cdots)q^{7}+\cdots\)
880.4.b.e	$880$	$4$	880.b	5.b	$2$	$6$	$6$	$51.922$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					220.4.b.b	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2-\beta _{1}+\beta _{4})q^{5}+\beta _{3}q^{7}+\cdots\)
880.4.b.f	$880$	$4$	880.b	5.b	$2$	$6$	$6$	$51.922$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					55.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+(-1-\beta _{2}+\beta _{3}+\beta _{5})q^{5}+\cdots\)
880.4.b.g	$880$	$4$	880.b	5.b	$2$	$6$	$6$	$51.922$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					220.4.b.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(3\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
880.4.b.h	$880$	$4$	880.b	5.b	$2$	$8$	$8$	$51.922$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					110.4.b.c	$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(2-\beta _{4})q^{5}+(\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
880.4.b.i	$880$	$4$	880.b	5.b	$2$	$10$	$10$	$51.922$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					55.4.b.b	$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{10}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(1+\beta _{6})q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
880.4.b.j	$880$	$4$	880.b	5.b	$2$	$20$	$20$	$51.922$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					440.4.b.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{39}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{5}q^{5}+\beta _{13}q^{7}+(-8+\beta _{1}+\cdots)q^{9}+\cdots\)
880.4.b.k	$880$	$4$	880.b	5.b	$2$	$24$	$24$	$51.922$		None			✓		440.4.b.c	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)