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

• Label: 880.2.bo
• Level: $880$
• Weight: $2$
• Character orbit: 880.bo
• Rep. character: $\chi_{880}(81,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $96$
• Newform subspaces: $11$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	624	96	528
Cusp forms	528	96	432
Eisenstein series	96	0	96

Trace form

96 * q + 4 * q^7 - 16 * q^9 + 4 * q^11 + 8 * q^17 + 8 * q^23 - 24 * q^25 - 16 * q^29 - 20 * q^33 - 12 * q^35 + 24 * q^37 + 36 * q^39 - 20 * q^41 + 56 * q^43 + 36 * q^47 - 36 * q^49 + 36 * q^51 + 40 * q^53 - 20 * q^57 - 16 * q^59 + 16 * q^61 + 20 * q^63 + 8 * q^65 + 40 * q^67 + 32 * q^69 - 28 * q^71 + 24 * q^73 - 24 * q^77 - 84 * q^79 - 68 * q^81 - 36 * q^83 - 168 * q^87 - 16 * q^89 - 64 * q^91 + 32 * q^93 + 16 * q^95 - 28 * q^97 - 112 * q^99

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.bo.a	$880$	$2$	880.bo	11.c	$5$	$4$	$1$	$7.027$	\(\Q(\zeta_{10})\)	None					110.2.g.a	$2$	$0$	\(0\)	\(-4\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+\zeta_{10}q^{5}+\cdots\)
880.2.bo.b	$880$	$2$	880.bo	11.c	$5$	$4$	$1$	$7.027$	\(\Q(\zeta_{10})\)	None					110.2.g.b	$2$	$0$	\(0\)	\(-4\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\zeta_{10}q^{5}+\cdots\)
880.2.bo.c	$880$	$2$	880.bo	11.c	$5$	$8$	$2$	$7.027$	8.0.159390625.1	None					220.2.m.b	$2$	$0$	\(0\)	\(-5\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{3}+\cdots\)
880.2.bo.d	$880$	$2$	880.bo	11.c	$5$	$8$	$2$	$7.027$	8.0.13140625.1	None					440.2.y.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}+\beta _{5})q^{3}+\beta _{7}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.e	$880$	$2$	880.bo	11.c	$5$	$8$	$2$	$7.027$	8.0.159390625.1	None					55.2.g.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(2-3\beta _{2}-3\beta _{3}+\cdots)q^{7}+\cdots\)
880.2.bo.f	$880$	$2$	880.bo	11.c	$5$	$8$	$2$	$7.027$	8.0.26265625.1	None					220.2.m.a	$2$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}+\beta _{7})q^{3}+\beta _{2}q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.g	$880$	$2$	880.bo	11.c	$5$	$8$	$2$	$7.027$	8.0.682515625.5	None					110.2.g.c	$2$	$0$	\(0\)	\(4\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{3}+\beta _{5}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
880.2.bo.h	$880$	$2$	880.bo	11.c	$5$	$8$	$2$	$7.027$	8.0.13140625.1	None					55.2.g.b	$2$	$0$	\(0\)	\(5\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{5}+\beta _{6})q^{3}+\cdots\)
880.2.bo.i	$880$	$2$	880.bo	11.c	$5$	$12$	$3$	$7.027$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					440.2.y.c	$2$	$0$	\(0\)	\(1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{3}-\beta _{8})q^{3}-\beta _{6}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.j	$880$	$2$	880.bo	11.c	$5$	$12$	$3$	$7.027$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					440.2.y.b	$2$	$0$	\(0\)	\(1\)	\(3\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{5})q^{3}+\beta _{8}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
880.2.bo.k	$880$	$2$	880.bo	11.c	$5$	$16$	$4$	$7.027$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		440.2.y.d	$2$	$0$	\(0\)	\(3\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots\)

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

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