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

• Label: 275.2.ba
• Level: $275$
• Weight: $2$
• Character orbit: 275.ba
• Rep. character: $\chi_{275}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $112$
• 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.ba (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{10})\)
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	128	128	0
Cusp forms	112	112	0
Eisenstein series	16	16	0

Trace form

112 * q - 5 * q^2 - 5 * q^3 + 25 * q^4 - 2 * q^5 - 13 * q^6 + 10 * q^7 + 5 * q^8 + 25 * q^9 - 20 * q^10 - 5 * q^11 + 20 * q^12 - 5 * q^13 + q^14 - 11 * q^15 - 17 * q^16 - 10 * q^17 + 15 * q^18 + 5 * q^19 - 38 * q^20 - 26 * q^21 - 15 * q^22 - 30 * q^23 - 18 * q^24 + 34 * q^25 - 34 * q^26 - 5 * q^27 + 11 * q^29 + 41 * q^30 - 4 * q^34 + 2 * q^35 + 14 * q^36 - 5 * q^37 - 15 * q^38 + 13 * q^39 + 2 * q^40 + 46 * q^41 + 3 * q^44 - 28 * q^45 - 13 * q^46 + 10 * q^47 + 24 * q^49 - 62 * q^50 - 19 * q^51 - 15 * q^52 + 60 * q^53 - 22 * q^54 - 8 * q^55 - 36 * q^56 - 40 * q^57 + 40 * q^58 - 2 * q^59 - 102 * q^60 - 28 * q^61 - 85 * q^62 - 33 * q^64 - 60 * q^65 - 25 * q^66 + 45 * q^67 - 145 * q^68 - 45 * q^69 + 11 * q^70 - 28 * q^71 + 5 * q^74 - 30 * q^75 + 100 * q^76 - 35 * q^77 - 70 * q^78 + 51 * q^79 - 126 * q^80 + 17 * q^81 + 10 * q^82 - 15 * q^83 + 100 * q^84 - 2 * q^85 - 43 * q^86 + 30 * q^87 + 85 * q^88 - 21 * q^89 - 72 * q^90 - 62 * q^91 + 110 * q^92 + 105 * q^93 - 16 * q^94 - 12 * q^95 + 53 * q^96 + 50 * q^97 + 25 * q^98 + 50 * 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.ba.a	$275$	$2$	275.ba	275.aa	$10$	$112$	$28$	$2.196$		None		✓	✓	✓	275.2.ba.a	$2$	$0$	\(-5\)	\(-5\)	\(-2\)	\(10\)		$\mathrm{SU}(2)[C_{10}]$