Space of modular forms of level 195, weight 2, and trivial character

• Label: 195.2.a
• Level: $195$
• Weight: $2$
• Character orbit: 195.a
• Rep. character: $\chi_{195}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $5$
• Sturm bound: $56$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(56\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(195))\).

	Total	New	Old
Modular forms	32	7	25
Cusp forms	25	7	18
Eisenstein series	7	0	7

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

\(3\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(-\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(2\)
Plus space			\(+\)	\(0\)
Minus space			\(-\)	\(7\)

Trace form

7 * q + 5 * q^2 - q^3 + 13 * q^4 - q^5 + q^6 + 9 * q^8 + 7 * q^9 + q^10 + 4 * q^11 - 7 * q^12 + 3 * q^13 - 8 * q^14 + 3 * q^15 + 13 * q^16 - 2 * q^17 + 5 * q^18 - 4 * q^19 - 7 * q^20 - 8 * q^21 - 12 * q^22 - 3 * q^24 + 7 * q^25 - 3 * q^26 - q^27 - 32 * q^28 + 26 * q^29 - 3 * q^30 - 8 * q^31 - 7 * q^32 + 4 * q^33 - 30 * q^34 + 13 * q^36 + 34 * q^37 - 36 * q^38 - q^39 - 3 * q^40 - 10 * q^41 - 8 * q^42 - 12 * q^43 - 36 * q^44 - q^45 - 32 * q^46 - 16 * q^47 - 31 * q^48 + 3 * q^49 + 5 * q^50 + 2 * q^51 + 5 * q^52 + 42 * q^53 + q^54 - 8 * q^55 - 16 * q^56 - 12 * q^57 + 22 * q^58 - 12 * q^59 + 5 * q^60 + 14 * q^61 + 24 * q^62 + 13 * q^64 - q^65 + 4 * q^66 + 4 * q^67 + 10 * q^68 + 20 * q^69 + 8 * q^70 + 8 * q^71 + 9 * q^72 - 2 * q^73 - 10 * q^74 - q^75 - 4 * q^76 + 40 * q^77 + q^78 + 4 * q^79 - 31 * q^80 + 7 * q^81 + 18 * q^82 - 4 * q^83 + 16 * q^84 + 14 * q^85 + 44 * q^86 - 6 * q^87 - 4 * q^88 + 6 * q^89 + q^90 - 4 * q^91 - 8 * q^92 - 8 * q^93 - 4 * q^95 - 35 * q^96 - 10 * q^97 + 13 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(195))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	13
195.2.a.a	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	None	✓	✓			195.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
195.2.a.b	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	None	✓	✓	✓	✓	195.2.a.b	$1$	$0$	\(2\)	\(-1\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
195.2.a.c	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	None	✓	✓	✓	✓	195.2.a.c	$1$	$0$	\(2\)	\(1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
195.2.a.d	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	None	✓	✓			195.2.a.d	$1$	$0$	\(2\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
195.2.a.e	$195$	$2$	195.a	1.a	$1$	$3$	$3$	$1.557$	3.3.316.1	None	✓	✓	✓	✓	195.2.a.e	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(1\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(195))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(195)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)