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

• Label: 361.2.k
• Level: $361$
• Weight: $2$
• Character orbit: 361.k
• Rep. character: $\chi_{361}(4,\cdot)$
• Character field: $\Q(\zeta_{171})$
• Dimension: $3348$
• Newform subspaces: $1$
• Sturm bound: $63$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.k (of order \(171\) and degree \(108\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 361 \)
Character field:			\(\Q(\zeta_{171})\)
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	3564	3564	0
Cusp forms	3348	3348	0
Eisenstein series	216	216	0

Trace form

3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * 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.k.a	$361$	$2$	361.k	361.k	$171$	$3348$	$31$	$2.883$		None		✓	✓	✓	361.2.k.a	$2$	$0$	\(-108\)	\(-111\)	\(-108\)	\(-111\)		$\mathrm{SU}(2)[C_{171}]$