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

• Label: 880.2.m
• Level: $880$
• Weight: $2$
• Character orbit: 880.m
• Rep. character: $\chi_{880}(879,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $7$
• Sturm bound: $288$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 220 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	156	36	120
Cusp forms	132	36	96
Eisenstein series	24	0	24

Trace form

\( 36 q + 36 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.2.m.a	$880$	$2$	880.m	220.g	$2$	$2$	$2$	$7.027$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-2\)	\(-3\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-q^{3}+(-1-\beta )q^{5}-2q^{9}+(-1+2\beta )q^{11}+\cdots\)
880.2.m.b	$880$	$2$	880.m	220.g	$2$	$2$	$2$	$7.027$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(2\)	\(-3\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{3}+(-1-\beta )q^{5}-2q^{9}+(1-2\beta )q^{11}+\cdots\)
880.2.m.c	$880$	$2$	880.m	220.g	$2$	$4$	$4$	$7.027$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-2\)	\(3\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(5+\cdots)q^{9}+\cdots\)
880.2.m.d	$880$	$2$	880.m	220.g	$2$	$4$	$4$	$7.027$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(2\)	\(3\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
880.2.m.e	$880$	$2$	880.m	220.g	$2$	$8$	$8$	$7.027$	8.0.303595776.1	None		$8$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-2+\beta _{2})q^{5}+\beta _{5}q^{7}+\beta _{6}q^{11}+\cdots\)
880.2.m.f	$880$	$2$	880.m	220.g	$2$	$8$	$8$	$7.027$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\zeta_{24})q^{5}+\zeta_{24}^{2}q^{7}-3q^{9}+\zeta_{24}^{5}q^{11}+\cdots\)
880.2.m.g	$880$	$2$	880.m	220.g	$2$	$8$	$8$	$7.027$	8.0.3317760000.9	None		$8$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}+(1-\beta _{2})q^{5}-\beta _{4}q^{7}+3q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)