Space of modular forms of level 195, weight 3, and Character 195.j

• Label: 195.3.j
• Level: $195$
• Weight: $3$
• Character orbit: 195.j
• Rep. character: $\chi_{195}(8,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $104$
• Newform subspaces: $4$
• Sturm bound: $84$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	195.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(84\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(195, [\chi])\).

	Total	New	Old
Modular forms	120	120	0
Cusp forms	104	104	0
Eisenstein series	16	16	0

Trace form

\( 104 q - 4 q^{3} - 192 q^{4} - 4 q^{6} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(195, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
195.3.j.a	$195$	$3$	195.j	195.j	$4$	$2$	$1$	$5.313$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{2}-3q^{3}+3q^{4}+5iq^{5}-3iq^{6}+\cdots\)
195.3.j.b	$195$	$3$	195.j	195.j	$4$	$2$	$1$	$5.313$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}-3iq^{3}+3q^{4}-5iq^{5}-3q^{6}+\cdots\)
195.3.j.c	$195$	$3$	195.j	195.j	$4$	$4$	$2$	$5.313$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}+2\zeta_{8}^{3})q^{2}+(2+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
195.3.j.d	$195$	$3$	195.j	195.j	$4$	$96$	$48$	$5.313$		None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$