Space of modular forms of level 275, weight 2, and Character 275.bm

• Label: 275.2.bm
• Level: $275$
• Weight: $2$
• Character orbit: 275.bm
• Rep. character: $\chi_{275}(7,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $128$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bm (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(275, [\chi])\).

	Total	New	Old
Modular forms	288	160	128
Cusp forms	192	128	64
Eisenstein series	96	32	64

Trace form

\( 128 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(275, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.2.bm.a	$275$	$2$	275.bm	55.l	$20$	$32$	$4$	$2.196$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
275.2.bm.b	$275$	$2$	275.bm	55.l	$20$	$32$	$4$	$2.196$		None		$4$	$0$	\(10\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
275.2.bm.c	$275$	$2$	275.bm	55.l	$20$	$64$	$8$	$2.196$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(275, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)