Space of modular forms of level 190, weight 4, and Character 190.f

• Label: 190.4.f
• Level: $190$
• Weight: $4$
• Character orbit: 190.f
• Rep. character: $\chi_{190}(37,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	190.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(190, [\chi])\).

	Total	New	Old
Modular forms	188	60	128
Cusp forms	172	60	112
Eisenstein series	16	0	16

Trace form

60 * q + 16 * q^5 + 8 * q^7 - 56 * q^11 - 960 * q^16 + 320 * q^17 + 588 * q^23 + 80 * q^25 - 304 * q^26 + 32 * q^28 + 96 * q^30 - 1448 * q^35 + 2160 * q^36 - 152 * q^38 + 1216 * q^42 - 88 * q^43 - 2656 * q^45 - 1720 * q^47 + 2656 * q^55 - 256 * q^57 - 3456 * q^61 + 32 * q^62 + 2896 * q^63 + 1888 * q^66 + 1280 * q^68 + 2976 * q^73 + 880 * q^76 - 172 * q^77 - 256 * q^80 - 1500 * q^81 + 992 * q^82 + 5380 * q^83 - 1516 * q^85 + 1544 * q^87 - 2352 * q^92 - 14408 * q^93 - 4 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(190, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
190.4.f.a	$190$	$4$	190.f	95.g	$4$	$60$	$30$	$11.210$		None		✓	✓	✓	190.4.f.a	$4$	$0$	\(0\)	\(0\)	\(16\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(190, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(190, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)