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

• Label: 190.2.b
• Level: $190$
• Weight: $2$
• Character orbit: 190.b
• Rep. character: $\chi_{190}(39,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	34	10	24
Cusp forms	26	10	16
Eisenstein series	8	0	8

Trace form

\( 10 q - 10 q^{4} + 2 q^{5} - 10 q^{9} + O(q^{10}) \)

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.b.a	$190$	$2$	190.b	5.b	$2$	$4$	$4$	$1.517$	\(\Q(\zeta_{8})\)	None		✓			190.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
190.2.b.b	$190$	$2$	190.b	5.b	$2$	$6$	$6$	$1.517$	6.0.5161984.1	None		✓	✓		190.2.b.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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