Space of modular forms of level 195, weight 6, and Character 195.bb

• Label: 195.6.bb
• Level: $195$
• Weight: $6$
• Character orbit: 195.bb
• Rep. character: $\chi_{195}(121,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	195.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(195, [\chi])\).

	Total	New	Old
Modular forms	288	92	196
Cusp forms	272	92	180
Eisenstein series	16	0	16

Trace form

92 * q - 18 * q^3 + 704 * q^4 - 546 * q^7 - 3726 * q^9 + 400 * q^10 - 1008 * q^11 - 1152 * q^12 - 1278 * q^13 + 3536 * q^14 - 11000 * q^16 + 3612 * q^17 + 5412 * q^19 + 11400 * q^20 - 3612 * q^22 - 3956 * q^23 - 57500 * q^25 - 22288 * q^26 + 2916 * q^27 - 60408 * q^28 - 5048 * q^29 + 3600 * q^30 + 55740 * q^32 - 2900 * q^35 + 57024 * q^36 - 12468 * q^37 - 9600 * q^38 - 21636 * q^39 + 38400 * q^40 + 8460 * q^42 + 61522 * q^43 - 114684 * q^46 - 35856 * q^48 + 38760 * q^49 - 15336 * q^51 - 98616 * q^52 - 33088 * q^53 - 64200 * q^55 + 66884 * q^56 + 109584 * q^58 + 223488 * q^59 - 15358 * q^61 - 53828 * q^62 + 44226 * q^63 - 203264 * q^64 - 63500 * q^65 + 136512 * q^66 - 13710 * q^67 - 141264 * q^68 + 21780 * q^69 + 250800 * q^71 + 94576 * q^74 + 11250 * q^75 - 406620 * q^76 - 165640 * q^77 + 142488 * q^78 - 355420 * q^79 + 414000 * q^80 - 301806 * q^81 + 258616 * q^82 - 368064 * q^84 - 185904 * q^87 - 47328 * q^88 + 409728 * q^89 - 64800 * q^90 + 505222 * q^91 + 646072 * q^92 + 302886 * q^93 + 347480 * q^94 - 20200 * q^95 - 381702 * q^97 + 424176 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(195, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
195.6.bb.a	$195$	$6$	195.bb	13.e	$6$	$44$	$22$	$31.275$		None		✓			195.6.bb.a	$2$	$0$	\(0\)	\(198\)	\(0\)	\(-858\)		$\mathrm{SU}(2)[C_{6}]$
195.6.bb.b	$195$	$6$	195.bb	13.e	$6$	$48$	$24$	$31.275$		None		✓	✓		195.6.bb.b	$2$	$0$	\(0\)	\(-216\)	\(0\)	\(312\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{6}^{\mathrm{old}}(195, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(195, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)