Space of modular forms of level 1190, weight 2, and Character 1190.g

• Label: 1190.2.g
• Level: $1190$
• Weight: $2$
• Character orbit: 1190.g
• Rep. character: $\chi_{1190}(169,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1190, [\chi])\).

	Total	New	Old
Modular forms	224	56	168
Cusp forms	208	56	152
Eisenstein series	16	0	16

Trace form

56 * q - 56 * q^4 + 56 * q^9 - 8 * q^15 + 56 * q^16 + 16 * q^19 + 16 * q^21 + 8 * q^25 - 16 * q^26 + 8 * q^30 + 8 * q^34 - 56 * q^36 + 56 * q^49 - 56 * q^51 + 32 * q^55 + 80 * q^59 + 8 * q^60 - 56 * q^64 + 32 * q^66 + 16 * q^69 - 8 * q^70 - 16 * q^76 + 88 * q^81 - 16 * q^84 - 32 * q^85 + 88 * q^86 - 56 * q^89 - 24 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1190, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1190.2.g.a	$1190$	$2$	1190.g	85.c	$2$	$4$	$4$	$9.502$	\(\Q(i, \sqrt{21})\)	None		✓			1190.2.g.a	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
1190.2.g.b	$1190$	$2$	1190.g	85.c	$2$	$4$	$4$	$9.502$	\(\Q(i, \sqrt{21})\)	None		✓			1190.2.g.a	$2$	$0$	\(0\)	\(2\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(1-\beta _{3})q^{3}-q^{4}+(1-2\beta _{2}+\cdots)q^{5}+\cdots\)
1190.2.g.c	$1190$	$2$	1190.g	85.c	$2$	$24$	$24$	$9.502$		None		✓			1190.2.g.c	$2$	$0$	\(0\)	\(-10\)	\(-4\)	\(-24\)		$\mathrm{SU}(2)[C_{2}]$
1190.2.g.d	$1190$	$2$	1190.g	85.c	$2$	$24$	$24$	$9.502$		None		✓			1190.2.g.c	$2$	$0$	\(0\)	\(10\)	\(4\)	\(24\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1190, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1190, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(595, [\chi])\)\(^{\oplus 2}\)