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

• Label: 361.2.g
• Level: $361$
• Weight: $2$
• Character orbit: 361.g
• Rep. character: $\chi_{361}(20,\cdot)$
• Character field: $\Q(\zeta_{19})$
• Dimension: $540$
• Newform subspaces: $1$
• Sturm bound: $63$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.g (of order \(19\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 361 \)
Character field:			\(\Q(\zeta_{19})\)
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	576	576	0
Cusp forms	540	540	0
Eisenstein series	36	36	0

Trace form

540 * q - 16 * q^2 - 32 * q^3 - 40 * q^4 - 17 * q^5 - 7 * q^6 - 11 * q^7 - 4 * q^8 - 94 * q^9 - 58 * q^10 - 11 * q^11 + 5 * q^12 - q^13 - 33 * q^14 + 11 * q^15 - 22 * q^16 - 56 * q^17 + 20 * q^18 - q^19 + 25 * q^20 + 11 * q^21 - 116 * q^22 + q^23 + 33 * q^24 - 23 * q^25 - 80 * q^26 - 2 * q^27 + 12 * q^28 - 33 * q^29 - 69 * q^30 + 17 * q^31 + 44 * q^32 - 3 * q^33 + 35 * q^34 + 27 * q^35 + 36 * q^36 + 17 * q^37 + 19 * q^38 - 53 * q^39 + 71 * q^40 + 29 * q^41 + 71 * q^42 - 169 * q^43 + 59 * q^44 - 44 * q^45 + 15 * q^46 - 32 * q^47 - 96 * q^48 - 67 * q^49 - 2 * q^50 - 29 * q^51 + 71 * q^52 + 23 * q^53 - 350 * q^54 + 35 * q^55 - 241 * q^56 + 59 * q^57 + 67 * q^58 + 47 * q^59 + 99 * q^60 + 39 * q^61 + 52 * q^62 - 20 * q^63 + 80 * q^64 + q^65 + 113 * q^66 + 53 * q^67 + 72 * q^68 - 246 * q^69 - 27 * q^70 + 47 * q^71 + 176 * q^72 + 53 * q^73 - 107 * q^74 - 115 * q^75 - 245 * q^76 + 69 * q^77 - 117 * q^78 + 53 * q^79 - 205 * q^80 - 54 * q^81 + 21 * q^82 + 26 * q^83 + 152 * q^84 + 83 * q^85 - 267 * q^86 + 8 * q^87 + 161 * q^88 - 55 * q^89 - 127 * q^90 + 51 * q^91 + 133 * q^92 + 93 * q^93 - 141 * q^94 - 22 * q^95 - 19 * q^96 + 14 * q^97 + 57 * q^98 + 94 * 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.g.a	$361$	$2$	361.g	361.g	$19$	$540$	$30$	$2.883$		None		✓	✓	✓	361.2.g.a	$2$	$0$	\(-16\)	\(-32\)	\(-17\)	\(-11\)		$\mathrm{SU}(2)[C_{19}]$