Space of modular forms of level 361, weight 2, and Character 361.i

• Label: 361.2.i
• Level: $361$
• Weight: $2$
• Character orbit: 361.i
• Rep. character: $\chi_{361}(7,\cdot)$
• Character field: $\Q(\zeta_{57})$
• Dimension: $1080$
• Newform subspaces: $1$
• Sturm bound: $63$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.i (of order \(57\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 361 \)
Character field:			\(\Q(\zeta_{57})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(63\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(361, [\chi])\).

	Total	New	Old
Modular forms	1152	1152	0
Cusp forms	1080	1080	0
Eisenstein series	72	72	0

Trace form

1080 * q - 38 * q^2 - 19 * q^3 - 8 * q^4 - 37 * q^5 - 38 * q^6 - 40 * q^7 - 38 * q^8 + 49 * q^9 + 19 * q^10 - 40 * q^11 - 38 * q^12 - 38 * q^13 - 38 * q^15 - 8 * q^16 - 94 * q^17 - 38 * q^18 - 38 * q^19 - 46 * q^20 - 38 * q^21 - 19 * q^22 - 34 * q^23 - 30 * q^24 - 7 * q^25 + 41 * q^26 - 76 * q^27 - 15 * q^28 + 60 * q^30 - 38 * q^31 - 38 * q^32 - 114 * q^33 - 38 * q^34 - 33 * q^35 - 38 * q^37 - 76 * q^38 + 26 * q^39 - 38 * q^40 - 38 * q^41 - 32 * q^42 + 43 * q^43 - 26 * q^44 + 47 * q^45 + 26 * q^47 - 456 * q^48 - 32 * q^49 + 38 * q^50 + 38 * q^51 - 38 * q^52 - 38 * q^53 - 214 * q^54 - 29 * q^55 + 304 * q^56 - 38 * q^57 - 46 * q^58 - 38 * q^59 - 33 * q^61 - 13 * q^62 + 68 * q^63 - 110 * q^64 + 38 * q^65 - 26 * q^66 - 38 * q^67 - 96 * q^68 - 228 * q^69 - 342 * q^70 - 38 * q^71 - 38 * q^72 - 29 * q^73 + 50 * q^74 + 190 * q^75 + 323 * q^76 - 60 * q^77 + 228 * q^78 - 38 * q^79 + 322 * q^80 + 129 * q^81 + 48 * q^82 - 35 * q^83 + 19 * q^84 - 23 * q^85 - 684 * q^86 + 37 * q^87 - 38 * q^88 + 76 * q^89 - 722 * q^90 - 114 * q^91 - 22 * q^92 - 30 * q^93 + 228 * q^94 - 152 * q^95 + 142 * q^96 + 19 * q^97 + 57 * q^98 + 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(361, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
361.2.i.a	$361$	$2$	361.i	361.i	$57$	$1080$	$30$	$2.883$		None		✓	✓	✓	361.2.i.a	$2$	$0$	\(-38\)	\(-19\)	\(-37\)	\(-40\)		$\mathrm{SU}(2)[C_{57}]$