Space of modular forms of level 95, weight 2, and trivial character

• Label: 95.2.a
• Level: $95$
• Weight: $2$
• Character orbit: 95.a
• Rep. character: $\chi_{95}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(20\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(95))\).

	Total	New	Old
Modular forms	12	7	5
Cusp forms	9	7	2
Eisenstein series	3	0	3

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
\(+\)	\(-\)	\(-\)		\(6\)	\(4\)	\(2\)		\(5\)	\(4\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(10\)	\(7\)	\(3\)		\(8\)	\(7\)	\(1\)		\(2\)	\(0\)	\(2\)

Trace form

7 * q - q^2 + 4 * q^3 + 9 * q^4 - q^5 - 4 * q^6 + 4 * q^7 - 9 * q^8 + 11 * q^9 + 3 * q^10 - 4 * q^11 - 4 * q^12 + 10 * q^13 - 12 * q^14 + q^16 + 6 * q^17 - 29 * q^18 + q^19 - 7 * q^20 - 16 * q^21 - 12 * q^22 - 12 * q^23 - 28 * q^24 + 7 * q^25 - 2 * q^26 + 4 * q^27 + 4 * q^28 - 6 * q^29 - 4 * q^30 + 8 * q^31 - 9 * q^32 + 12 * q^33 + 14 * q^34 - 4 * q^35 + 29 * q^36 + 14 * q^37 - 3 * q^38 - 8 * q^39 + 15 * q^40 + 14 * q^41 + 16 * q^42 + 12 * q^44 - 5 * q^45 + 12 * q^46 - 12 * q^47 + 48 * q^48 + 31 * q^49 - q^50 - 32 * q^51 + 22 * q^52 + 6 * q^53 - 12 * q^55 + 4 * q^56 + 2 * q^58 - 20 * q^59 - 16 * q^60 + 18 * q^61 + 48 * q^62 - 12 * q^63 - 15 * q^64 + 6 * q^65 - 8 * q^66 - 16 * q^67 + 2 * q^68 + 16 * q^69 + 4 * q^70 - 24 * q^71 - 65 * q^72 + 30 * q^73 + 30 * q^74 + 4 * q^75 + 7 * q^76 - 32 * q^77 - 16 * q^79 - 7 * q^80 + 15 * q^81 - 2 * q^82 - 32 * q^83 - 24 * q^84 - 2 * q^85 - 24 * q^86 - 64 * q^87 - 16 * q^88 + 6 * q^89 + 39 * q^90 - 16 * q^91 - 20 * q^92 - 56 * q^93 - 52 * q^94 - 7 * q^95 - 28 * q^96 + 50 * q^97 + 23 * q^98 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(95))\) 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
95.2.a.a	$95$	$2$	95.a	1.a	$1$	$3$	$3$	$0.759$	3.3.148.1	None	✓	✓	✓	✓	95.2.a.a	$1$	$0$	\(1\)	\(2\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
95.2.a.b	$95$	$2$	95.a	1.a	$1$	$4$	$4$	$0.759$	4.4.11344.1	None	✓	✓	✓	✓	95.2.a.b	$1$	$0$	\(-2\)	\(2\)	\(-4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(95))\) into lower level spaces

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