Space of modular forms of level 95, weight 11, and Character 95.m

• Label: 95.11.m
• Level: $95$
• Weight: $11$
• Character orbit: 95.m
• Rep. character: $\chi_{95}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $392$
• Newform subspaces: $1$
• Sturm bound: $110$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.m (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(110\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(95, [\chi])\).

	Total	New	Old
Modular forms	408	408	0
Cusp forms	392	392	0
Eisenstein series	16	16	0

Trace form

392 * q - 2 * q^2 - 2 * q^3 + 2220 * q^5 + 4856 * q^6 + 7780 * q^7 - 142356 * q^8 - 2 * q^10 + 32064 * q^11 - 232108 * q^12 - 818490 * q^13 - 1141388 * q^15 + 49026272 * q^16 + 2072126 * q^17 + 4464336 * q^18 - 30123952 * q^20 - 1448284 * q^21 + 4905706 * q^22 + 131242 * q^23 - 5318128 * q^25 + 35863504 * q^26 - 40337048 * q^27 + 35162792 * q^28 - 626212 * q^30 - 64672896 * q^31 + 101446340 * q^32 + 16944736 * q^33 + 97780658 * q^35 - 1696907108 * q^36 + 188603000 * q^37 + 316760754 * q^38 + 440672472 * q^40 - 428613964 * q^41 - 774149798 * q^42 - 203275548 * q^43 + 445246440 * q^45 - 1583809336 * q^46 + 827682184 * q^47 + 93769212 * q^48 + 3444668164 * q^50 - 375042204 * q^51 - 1680459778 * q^52 - 312762144 * q^53 - 922476300 * q^55 + 1245970416 * q^56 - 1399302072 * q^57 + 5178550404 * q^58 + 2790379518 * q^60 + 2729471636 * q^61 + 1463639316 * q^62 - 5716734310 * q^63 - 5741012704 * q^65 - 14278935268 * q^66 - 1123450394 * q^67 + 2843511172 * q^68 + 5385951110 * q^70 + 3202662556 * q^71 - 10998992704 * q^72 + 4692302722 * q^73 + 35410377548 * q^75 - 4934546772 * q^76 + 13472322668 * q^77 + 3477052916 * q^78 - 3697722930 * q^80 + 61033508952 * q^81 - 14484700660 * q^82 + 6779152124 * q^83 - 20028400922 * q^85 + 24296217656 * q^86 - 17074613364 * q^87 + 9785438184 * q^88 - 10206419488 * q^90 + 46291684236 * q^91 - 17646129964 * q^92 - 14290061476 * q^93 - 9651375010 * q^95 - 147008832576 * q^96 - 12701510184 * q^97 - 535132524 * q^98

Decomposition of \(S_{11}^{\mathrm{new}}(95, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.11.m.a	$95$	$11$	95.m	95.m	$12$	$392$	$98$	$60.359$		None		✓	✓	✓	95.11.m.a	$4$	$0$	\(-2\)	\(-2\)	\(2220\)	\(7780\)		$\mathrm{SU}(2)[C_{12}]$