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

• Label: 190.2.r
• Level: $190$
• Weight: $2$
• Character orbit: 190.r
• Rep. character: $\chi_{190}(3,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $120$
• 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.r (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{36})\)
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	408	120	288
Cusp forms	312	120	192
Eisenstein series	96	0	96

Trace form

120 * q - 12 * q^7 - 36 * q^15 + 36 * q^17 - 96 * q^21 + 24 * q^22 - 24 * q^25 - 12 * q^26 - 96 * q^33 + 36 * q^35 - 12 * q^41 - 72 * q^43 - 36 * q^45 - 24 * q^47 - 144 * q^50 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 84 * q^57 - 24 * q^60 + 48 * q^61 - 24 * q^62 + 36 * q^63 - 180 * q^65 - 24 * q^66 - 96 * q^67 - 12 * q^68 - 48 * q^70 - 36 * q^73 + 12 * q^76 + 96 * q^78 + 144 * q^81 + 48 * q^82 + 24 * q^83 + 48 * q^85 + 48 * q^86 + 72 * q^87 + 168 * q^90 + 72 * q^91 + 72 * q^92 + 156 * q^93 + 24 * q^95 + 120 * q^97 + 24 * q^98

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.r.a	$190$	$2$	190.r	95.r	$36$	$120$	$10$	$1.517$		None		✓	✓	✓	190.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{36}]$

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

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