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

• Label: 275.2.bn
• Level: $275$
• Weight: $2$
• Character orbit: 275.bn
• Rep. character: $\chi_{275}(2,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $224$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bn (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

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

\( 224 q - 10 q^{2} - 4 q^{3} - 10 q^{4} - 2 q^{5} - 10 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} + O(q^{10}) \)

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.bn.a	$275$	$2$	275.bn	275.an	$20$	$224$	$28$	$2.196$		None		$2$	$0$	\(-10\)	\(-4\)	\(-2\)	\(-10\)		$\mathrm{SU}(2)[C_{20}]$