Space of modular forms of level 195, weight 2, and Character 195.b

• Label: 195.2.b
• Level: $195$
• Weight: $2$
• Character orbit: 195.b
• Rep. character: $\chi_{195}(181,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $56$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(56\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(195, [\chi])\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	24	8	16
Eisenstein series	8	0	8

Trace form

8 * q + 4 * q^3 - 4 * q^4 + 8 * q^9 - 4 * q^10 - 12 * q^12 + 4 * q^13 - 16 * q^14 + 12 * q^16 + 24 * q^22 - 8 * q^23 - 8 * q^25 - 16 * q^26 + 4 * q^27 - 8 * q^29 - 4 * q^30 - 8 * q^35 - 4 * q^36 + 24 * q^38 - 4 * q^39 + 12 * q^40 - 16 * q^42 - 16 * q^43 - 4 * q^48 + 4 * q^49 - 12 * q^51 + 4 * q^52 - 16 * q^53 + 20 * q^55 + 56 * q^56 - 20 * q^61 - 8 * q^62 - 12 * q^64 - 8 * q^65 + 24 * q^66 + 24 * q^68 + 4 * q^69 + 40 * q^74 - 4 * q^75 + 56 * q^77 - 16 * q^78 - 28 * q^79 + 8 * q^81 + 16 * q^82 + 16 * q^87 - 80 * q^88 - 4 * q^90 - 52 * q^91 - 80 * q^92 - 16 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(195, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
195.2.b.a	$195$	$2$	195.b	13.b	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	None		✓			195.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2 q^{4}+i q^{5}+3 i q^{7}+q^{9}+\cdots\)
195.2.b.b	$195$	$2$	195.b	13.b	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	None		✓			195.2.b.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}+q^{4}+i q^{5}+i q^{6}+\cdots\)
195.2.b.c	$195$	$2$	195.b	13.b	$2$	$4$	$4$	$1.557$	\(\Q(i, \sqrt{17})\)	None		✓	✓		195.2.b.c	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(195, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(195, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)