Space of modular forms of level 363, weight 2, and Character 363.p

• Label: 363.2.p
• Level: $363$
• Weight: $2$
• Character orbit: 363.p
• Rep. character: $\chi_{363}(2,\cdot)$
• Character field: $\Q(\zeta_{110})$
• Dimension: $1680$
• Newform subspaces: $1$
• Sturm bound: $88$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.p (of order \(110\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 363 \)
Character field:			\(\Q(\zeta_{110})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(88\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(363, [\chi])\).

	Total	New	Old
Modular forms	1840	1840	0
Cusp forms	1680	1680	0
Eisenstein series	160	160	0

Trace form

1680 * q - 28 * q^3 - 42 * q^4 - 66 * q^6 - 78 * q^7 - 42 * q^9 - 66 * q^10 - 40 * q^12 - 56 * q^13 - 96 * q^15 - 50 * q^16 - 66 * q^18 - 108 * q^19 - 11 * q^21 - 152 * q^22 + 21 * q^24 - 134 * q^25 - 25 * q^27 - 88 * q^28 + 9 * q^30 - 52 * q^31 - 73 * q^33 - 64 * q^34 + 4 * q^36 - 84 * q^37 - 31 * q^39 - 110 * q^40 - 87 * q^42 - 88 * q^43 - 87 * q^45 - 118 * q^46 - 37 * q^48 - 184 * q^49 - 96 * q^51 - 120 * q^52 + 88 * q^54 - 144 * q^55 + 96 * q^57 - 144 * q^58 - 85 * q^60 - 78 * q^61 + 118 * q^63 - 202 * q^64 + 30 * q^66 - 92 * q^67 - 56 * q^69 - 146 * q^70 - 112 * q^72 - 66 * q^73 - 17 * q^75 - 286 * q^76 - 65 * q^78 - 182 * q^79 - 34 * q^81 - 30 * q^82 - 11 * q^84 + 34 * q^85 - 77 * q^87 - 336 * q^88 - 73 * q^90 + 54 * q^91 - 51 * q^93 - 80 * q^94 - 87 * q^96 - 92 * q^97 - 159 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(363, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
363.2.p.a	$363$	$2$	363.p	363.p	$110$	$1680$	$42$	$2.899$		None		✓	✓	✓	363.2.p.a	$4$	$0$	\(0\)	\(-28\)	\(0\)	\(-78\)		$\mathrm{SU}(2)[C_{110}]$