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

• Label: 195.2.m
• Level: $195$
• Weight: $2$
• Character orbit: 195.m
• Rep. character: $\chi_{195}(53,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	64	48	16
Cusp forms	48	48	0
Eisenstein series	16	0	16

Trace form

48 * q - 4 * q^3 - 8 * q^6 - 8 * q^7 + 16 * q^12 - 4 * q^15 - 40 * q^16 - 28 * q^18 - 16 * q^21 - 8 * q^25 - 16 * q^27 + 8 * q^28 + 28 * q^30 - 16 * q^31 + 4 * q^33 + 24 * q^36 + 40 * q^37 + 8 * q^40 - 20 * q^42 + 16 * q^43 - 44 * q^45 + 68 * q^48 - 48 * q^51 - 8 * q^52 - 20 * q^57 - 88 * q^58 + 36 * q^60 - 24 * q^61 + 48 * q^63 + 88 * q^66 - 8 * q^67 - 120 * q^70 + 36 * q^72 + 8 * q^73 - 12 * q^75 - 16 * q^76 + 88 * q^82 - 20 * q^87 + 48 * q^88 + 20 * q^90 + 8 * q^91 - 20 * q^93 - 96 * q^97

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.m.a	$195$	$2$	195.m	15.e	$4$	$48$	$24$	$1.557$		None		✓	✓	✓	195.2.m.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$