Space of modular forms of level 190, weight 4, and trivial character

• Label: 190.4.a
• Level: $190$
• Weight: $4$
• Character orbit: 190.a
• Rep. character: $\chi_{190}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $9$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	190.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(190))\).

	Total	New	Old
Modular forms	94	18	76
Cusp forms	86	18	68
Eisenstein series	8	0	8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(15\)	\(2\)	\(13\)		\(14\)	\(2\)	\(12\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(9\)	\(3\)	\(6\)		\(8\)	\(3\)	\(5\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(10\)	\(1\)	\(9\)		\(9\)	\(1\)	\(8\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(13\)	\(3\)	\(10\)		\(12\)	\(3\)	\(9\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(14\)	\(3\)	\(11\)		\(13\)	\(3\)	\(10\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(9\)	\(2\)	\(7\)		\(8\)	\(2\)	\(6\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(11\)	\(3\)	\(8\)		\(10\)	\(3\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(13\)	\(1\)	\(12\)		\(12\)	\(1\)	\(11\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(48\)	\(10\)	\(38\)		\(44\)	\(10\)	\(34\)		\(4\)	\(0\)	\(4\)
Minus space			\(-\)		\(46\)	\(8\)	\(38\)		\(42\)	\(8\)	\(34\)		\(4\)	\(0\)	\(4\)

Trace form

18 * q + 72 * q^4 - 10 * q^5 - 8 * q^6 + 126 * q^9 - 96 * q^11 - 32 * q^13 + 88 * q^14 + 80 * q^15 + 288 * q^16 - 72 * q^17 - 224 * q^18 - 40 * q^20 - 232 * q^21 - 128 * q^23 - 32 * q^24 + 450 * q^25 + 160 * q^26 - 48 * q^27 + 220 * q^29 + 160 * q^30 - 472 * q^31 + 496 * q^33 - 144 * q^34 - 220 * q^35 + 504 * q^36 - 192 * q^37 - 228 * q^38 + 28 * q^39 + 1756 * q^41 + 280 * q^42 - 972 * q^43 - 384 * q^44 - 50 * q^45 - 840 * q^46 - 1292 * q^47 - 666 * q^49 + 2296 * q^51 - 128 * q^52 + 1904 * q^53 + 472 * q^54 - 120 * q^55 + 352 * q^56 - 228 * q^57 - 568 * q^58 - 528 * q^59 + 320 * q^60 + 188 * q^61 - 1360 * q^62 + 1100 * q^63 + 1152 * q^64 + 960 * q^65 + 864 * q^66 + 712 * q^67 - 288 * q^68 - 552 * q^69 + 360 * q^70 - 1208 * q^71 - 896 * q^72 - 1424 * q^73 - 360 * q^74 + 144 * q^77 - 1760 * q^78 - 208 * q^79 - 160 * q^80 + 1282 * q^81 - 1248 * q^82 - 1788 * q^83 - 928 * q^84 - 660 * q^85 - 2424 * q^86 - 2300 * q^87 - 2860 * q^89 + 800 * q^91 - 512 * q^92 + 128 * q^93 + 1016 * q^94 - 128 * q^96 - 3728 * q^97 + 4576 * q^98 - 3520 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(190))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	19
190.4.a.a	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	\(\Q\)	None	✓	✓			190.4.a.a	$1$	$0$	\(-2\)	\(-2\)	\(5\)	\(8\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots\)
190.4.a.b	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	\(\Q\)	None	✓	✓	✓	✓	190.4.a.b	$1$	$1$	\(-2\)	\(2\)	\(5\)	\(-12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots\)
190.4.a.c	$190$	$4$	190.a	1.a	$1$	$1$	$1$	$11.210$	\(\Q\)	None	✓	✓	✓	✓	190.4.a.c	$1$	$1$	\(2\)	\(-4\)	\(5\)	\(-20\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots\)
190.4.a.d	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	\(\Q(\sqrt{313}) \)	None	✓	✓	✓		190.4.a.d	$1$	$0$	\(-4\)	\(1\)	\(10\)	\(-27\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots\)
190.4.a.e	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	190.4.a.e	$1$	$0$	\(-4\)	\(2\)	\(-10\)	\(8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.f	$190$	$4$	190.a	1.a	$1$	$2$	$2$	$11.210$	\(\Q(\sqrt{34}) \)	None	✓	✓	✓	✓	190.4.a.f	$1$	$0$	\(4\)	\(0\)	\(-10\)	\(24\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots\)
190.4.a.g	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.126168.1	None	✓	✓	✓	✓	190.4.a.g	$1$	$1$	\(-6\)	\(-1\)	\(-15\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots\)
190.4.a.h	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.5468.1	None	✓	✓	✓	✓	190.4.a.h	$1$	$1$	\(6\)	\(-9\)	\(-15\)	\(-11\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.i	$190$	$4$	190.a	1.a	$1$	$3$	$3$	$11.210$	3.3.15357.1	None	✓	✓	✓	✓	190.4.a.i	$1$	$0$	\(6\)	\(11\)	\(15\)	\(29\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(190))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(190)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)