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

• Label: 275.2.bo
• Level: $275$
• Weight: $2$
• Character orbit: 275.bo
• Rep. character: $\chi_{275}(87,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $224$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bo (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	256	256	0
Cusp forms	224	224	0
Eisenstein series	32	32	0

Trace form

\( 224 q - 14 q^{3} - 20 q^{4} - 12 q^{5} - 20 q^{9} + O(q^{10}) \)

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.bo.a	$275$	$2$	275.bo	275.ao	$20$	$16$	$2$	$2.196$	16.0.\(\cdots\).1	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(\beta _{1}+\beta _{4}+\beta _{5}+\beta _{7}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)
275.2.bo.b	$275$	$2$	275.bo	275.ao	$20$	$208$	$26$	$2.196$		None		$4$	$0$	\(0\)	\(-16\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$