Space of modular forms of level 190, weight 2, and Character 190.p

• Label: 190.2.p
• Level: $190$
• Weight: $2$
• Character orbit: 190.p
• Rep. character: $\chi_{190}(9,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.p (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(190, [\chi])\).

	Total	New	Old
Modular forms	204	60	144
Cusp forms	156	60	96
Eisenstein series	48	0	48

Trace form

60 * q + 12 * q^11 - 12 * q^14 - 30 * q^15 - 48 * q^19 - 12 * q^20 + 48 * q^21 - 24 * q^25 + 6 * q^26 - 24 * q^29 - 30 * q^35 + 48 * q^39 - 6 * q^41 + 6 * q^44 + 30 * q^45 - 30 * q^49 + 24 * q^50 - 180 * q^51 - 36 * q^54 + 54 * q^55 - 48 * q^56 + 36 * q^59 + 30 * q^60 - 120 * q^61 + 30 * q^64 + 30 * q^65 - 156 * q^66 - 48 * q^69 + 60 * q^70 + 18 * q^74 - 6 * q^76 + 12 * q^79 + 120 * q^81 + 12 * q^84 + 72 * q^85 + 24 * q^86 + 60 * q^89 + 36 * q^90 - 12 * q^91 + 156 * q^94 + 24 * q^95 + 198 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(190, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
190.2.p.a	$190$	$2$	190.p	95.p	$18$	$60$	$10$	$1.517$		None		✓	✓	✓	190.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(190, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(190, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)