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

• Label: 195.2.t
• Level: $195$
• Weight: $2$
• Character orbit: 195.t
• Rep. character: $\chi_{195}(73,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $28$
• 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.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
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	28	36
Cusp forms	48	28	20
Eisenstein series	16	0	16

Trace form

28 * q - 4 * q^2 + 28 * q^4 - 4 * q^5 - 12 * q^8 - 8 * q^11 - 8 * q^12 - 4 * q^15 + 28 * q^16 + 28 * q^17 + 12 * q^20 + 8 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^25 - 16 * q^31 - 68 * q^32 - 8 * q^33 - 28 * q^34 - 8 * q^39 - 48 * q^40 + 4 * q^41 - 40 * q^44 - 8 * q^45 - 16 * q^46 - 16 * q^48 + 28 * q^49 + 4 * q^50 + 48 * q^52 + 20 * q^53 - 8 * q^55 - 32 * q^59 - 60 * q^60 + 8 * q^61 - 72 * q^62 + 28 * q^64 + 64 * q^65 + 16 * q^66 + 32 * q^67 + 60 * q^68 - 8 * q^69 - 16 * q^70 + 40 * q^71 + 56 * q^73 + 16 * q^75 - 40 * q^76 + 48 * q^77 + 40 * q^78 - 12 * q^80 - 28 * q^81 - 4 * q^82 + 32 * q^84 + 44 * q^85 + 16 * q^86 - 24 * q^87 - 72 * q^88 + 36 * q^89 + 12 * q^90 - 56 * q^91 - 32 * q^92 - 56 * q^95 + 48 * q^97 - 12 * q^98 - 8 * 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.t.a	$195$	$2$	195.t	65.k	$4$	$28$	$14$	$1.557$		None		✓	✓	✓	195.2.k.a	$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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