Space of modular forms of level 195, weight 4, and Character 195.bl

• Label: 195.4.bl
• Level: $195$
• Weight: $4$
• Character orbit: 195.bl
• Rep. character: $\chi_{195}(68,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $320$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	195.bl (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(195, [\chi])\).

	Total	New	Old
Modular forms	352	352	0
Cusp forms	320	320	0
Eisenstein series	32	32	0

Trace form

320 * q - 2 * q^3 - 4 * q^6 - 4 * q^7 + 68 * q^10 - 148 * q^12 + 64 * q^13 - 2 * q^15 + 2168 * q^16 - 8 * q^18 + 208 * q^21 + 148 * q^22 - 16 * q^25 + 544 * q^27 - 548 * q^28 + 416 * q^30 + 112 * q^31 + 734 * q^33 - 1236 * q^36 - 796 * q^37 - 1416 * q^40 + 560 * q^42 + 740 * q^43 + 188 * q^45 + 136 * q^46 - 524 * q^48 + 2256 * q^51 - 164 * q^52 + 1120 * q^55 - 2980 * q^57 + 324 * q^58 - 3624 * q^60 + 1816 * q^61 - 1758 * q^63 + 2864 * q^66 + 2060 * q^67 - 1704 * q^70 - 1122 * q^72 - 736 * q^73 + 726 * q^75 + 1272 * q^76 - 4176 * q^78 - 852 * q^81 - 7412 * q^82 - 1108 * q^85 + 2354 * q^87 - 852 * q^88 - 6908 * q^90 - 1936 * q^91 + 2684 * q^93 + 7680 * q^96 - 1540 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(195, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
195.4.bl.a	$195$	$4$	195.bl	195.al	$12$	$320$	$80$	$11.505$		None		✓	✓	✓	195.4.bl.a	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$