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

• Label: 275.2.bf
• Level: $275$
• Weight: $2$
• Character orbit: 275.bf
• Rep. character: $\chi_{275}(28,\cdot)$
• 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.bf (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 - 14 * q^3 - 2 * q^5 - 10 * q^6 - 10 * q^7 + 10 * q^8 - 20 * q^9 + 20 * q^10 - 6 * q^11 - 38 * q^12 - 30 * q^13 - 10 * q^14 - 6 * q^15 - 188 * q^16 - 40 * q^18 - 20 * q^19 + 6 * q^20 + 30 * q^22 - 34 * q^23 + 40 * q^24 - 24 * q^25 - 12 * q^26 - 56 * q^27 - 10 * q^28 - 20 * q^29 - 10 * q^30 - 2 * q^31 + 70 * q^32 + 16 * q^33 - 20 * q^34 - 40 * q^35 + 42 * q^36 - 48 * q^37 - 70 * q^38 - 10 * q^39 + 30 * q^40 - 10 * q^41 - 90 * q^42 + 30 * q^44 + 52 * q^45 - 10 * q^46 - 38 * q^47 + 156 * q^48 + 110 * q^49 + 70 * q^50 - 20 * q^51 + 110 * q^52 + 106 * q^53 + 26 * q^55 - 4 * q^56 + 30 * q^57 + 10 * q^58 - 10 * q^59 + 134 * q^60 - 10 * q^61 + 50 * q^62 - 90 * q^63 - 30 * q^66 - 18 * q^67 + 30 * q^68 - 70 * q^70 + 18 * q^71 + 10 * q^72 - 10 * q^73 + 110 * q^74 - 6 * q^75 - 10 * q^77 - 80 * q^78 + 70 * q^79 - 212 * q^80 - 8 * q^81 - 10 * q^82 - 110 * q^83 - 70 * q^84 - 150 * q^85 - 12 * q^86 - 30 * q^87 + 110 * q^88 - 20 * q^89 - 10 * q^90 - 2 * q^91 + 172 * q^92 + 102 * q^93 - 170 * q^94 - 60 * q^95 + 30 * q^96 - 8 * q^97 - 80 * q^98 - 220 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.2.bf.a	$275$	$2$	275.bf	275.af	$20$	$224$	$28$	$2.196$		None		✓	✓	✓	275.2.bf.a	$2$	$0$	\(-10\)	\(-14\)	\(-2\)	\(-10\)		$\mathrm{SU}(2)[C_{20}]$