Space of modular forms of level 95, weight 4, and trivial character

• Label: 95.4.a
• Level: $95$
• Weight: $4$
• Character orbit: 95.a
• Rep. character: $\chi_{95}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $7$
• Sturm bound: $40$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(40\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(95))\).

	Total	New	Old
Modular forms	32	18	14
Cusp forms	28	18	10
Eisenstein series	4	0	4

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

\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(11\)	\(6\)	\(5\)		\(10\)	\(6\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(7\)	\(3\)	\(4\)		\(6\)	\(3\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(9\)	\(7\)	\(2\)		\(8\)	\(7\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(20\)	\(13\)	\(7\)		\(18\)	\(13\)	\(5\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(12\)	\(5\)	\(7\)		\(10\)	\(5\)	\(5\)		\(2\)	\(0\)	\(2\)

Trace form

18 * q + 4 * q^2 + 52 * q^4 + 10 * q^5 + 68 * q^6 + 28 * q^7 - 48 * q^8 + 166 * q^9 + 8 * q^11 + 64 * q^12 + 16 * q^13 - 24 * q^14 - 40 * q^15 + 484 * q^16 + 104 * q^17 - 108 * q^18 + 80 * q^20 + 240 * q^21 + 208 * q^22 + 12 * q^23 + 620 * q^24 + 450 * q^25 - 868 * q^26 + 288 * q^27 - 124 * q^28 + 220 * q^29 - 120 * q^30 + 344 * q^31 - 1720 * q^32 - 496 * q^33 - 592 * q^34 + 320 * q^35 - 1200 * q^36 + 112 * q^37 + 228 * q^38 - 116 * q^39 - 1084 * q^41 - 2796 * q^42 + 248 * q^43 - 792 * q^44 - 390 * q^45 - 512 * q^46 + 2024 * q^47 - 940 * q^48 + 1854 * q^49 + 100 * q^50 + 216 * q^51 + 436 * q^52 - 2432 * q^53 - 204 * q^54 + 320 * q^55 - 104 * q^56 + 228 * q^57 - 1132 * q^58 - 928 * q^59 + 340 * q^60 + 68 * q^61 + 136 * q^62 + 1392 * q^63 + 1332 * q^64 - 480 * q^65 + 2168 * q^66 + 1544 * q^67 + 1564 * q^68 + 1232 * q^69 - 1600 * q^70 - 1080 * q^71 - 908 * q^72 + 1040 * q^73 - 584 * q^74 + 768 * q^77 - 2792 * q^78 - 544 * q^79 - 360 * q^80 + 2810 * q^81 + 3744 * q^82 + 512 * q^83 + 1312 * q^84 + 500 * q^85 + 3448 * q^86 + 876 * q^87 + 3196 * q^88 + 3300 * q^89 + 1952 * q^91 + 4604 * q^92 + 4560 * q^93 - 3176 * q^94 + 760 * q^95 - 2980 * q^96 + 2512 * q^97 - 380 * q^98 + 664 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(95))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	19
95.4.a.a	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	\(\Q\)	None	✓	✓			95.4.a.a	$1$	$1$	\(0\)	\(4\)	\(-5\)	\(-22\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-8q^{4}-5q^{5}-22q^{7}-11q^{9}+\cdots\)
95.4.a.b	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	\(\Q\)	None	✓	✓			95.4.a.b	$1$	$1$	\(3\)	\(-5\)	\(-5\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-5q^{3}+q^{4}-5q^{5}-15q^{6}+\cdots\)
95.4.a.c	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	\(\Q\)	None	✓	✓			95.4.a.c	$1$	$0$	\(3\)	\(7\)	\(5\)	\(11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+7q^{3}+q^{4}+5q^{5}+21q^{6}+\cdots\)
95.4.a.d	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	\(\Q\)	None	✓	✓			95.4.a.d	$1$	$0$	\(5\)	\(4\)	\(5\)	\(-32\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{2}+4q^{3}+17q^{4}+5q^{5}+20q^{6}+\cdots\)
95.4.a.e	$95$	$4$	95.a	1.a	$1$	$3$	$3$	$5.605$	3.3.1304.1	None	✓	✓	✓	✓	95.4.a.e	$1$	$1$	\(-3\)	\(-11\)	\(15\)	\(-5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{2})q^{3}+\cdots\)
95.4.a.f	$95$	$4$	95.a	1.a	$1$	$5$	$5$	$5.605$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓		95.4.a.f	$1$	$0$	\(-3\)	\(-4\)	\(25\)	\(72\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
95.4.a.g	$95$	$4$	95.a	1.a	$1$	$6$	$6$	$5.605$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	95.4.a.g	$1$	$0$	\(-1\)	\(5\)	\(-30\)	\(5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(95))\) into lower level spaces

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