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

• Label: 195.2.bh
• Level: $195$
• Weight: $2$
• Character orbit: 195.bh
• Rep. character: $\chi_{195}(59,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• 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.bh (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(\zeta_{12})\)
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	128	128	0
Cusp forms	96	96	0
Eisenstein series	32	32	0

Trace form

96 * q - 24 * q^4 - 4 * q^9 - 36 * q^10 + 10 * q^15 - 16 * q^21 - 28 * q^24 + 18 * q^30 - 40 * q^31 - 32 * q^34 - 60 * q^36 - 4 * q^39 + 40 * q^40 + 4 * q^45 - 128 * q^46 + 60 * q^54 + 28 * q^55 + 20 * q^60 - 48 * q^61 - 8 * q^66 + 72 * q^69 + 168 * q^70 + 66 * q^75 - 80 * q^76 - 80 * q^79 + 48 * q^81 - 132 * q^84 - 20 * q^85 - 56 * q^91 + 72 * q^94 + 204 * q^96 - 48 * q^99

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.bh.a	$195$	$2$	195.bh	195.ah	$12$	$96$	$24$	$1.557$		None		✓	✓	✓	195.2.bh.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$