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

• Label: 95.11.q
• Level: $95$
• Weight: $11$
• Character orbit: 95.q
• Rep. character: $\chi_{95}(17,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $1176$
• Newform subspaces: $1$
• Sturm bound: $110$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.q (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{36})\)
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	1224	1224	0
Cusp forms	1176	1176	0
Eisenstein series	48	48	0

Trace form

1176 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 14604 * q^6 - 11688 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 + 3424146 * q^15 - 13618884 * q^16 - 3657378 * q^17 - 23774232 * q^18 + 38894436 * q^20 - 8689704 * q^21 - 22604556 * q^22 - 32885808 * q^23 + 42291732 * q^25 - 319452 * q^26 - 6 * q^27 + 144277488 * q^28 - 6 * q^30 - 12 * q^31 - 304326750 * q^32 + 265207902 * q^33 - 173435754 * q^35 - 288159144 * q^36 - 24 * q^37 + 1298228634 * q^38 - 1334600346 * q^40 + 659462736 * q^41 + 362797044 * q^42 - 961639656 * q^43 + 161157936 * q^45 - 12 * q^46 - 886017372 * q^47 + 1630739472 * q^48 + 2215521786 * q^50 + 1125126576 * q^51 + 6132 * q^52 - 657601770 * q^53 - 3332318022 * q^55 - 48 * q^56 - 967967226 * q^57 - 7596060648 * q^58 + 3688833012 * q^60 + 1851266016 * q^61 + 845228664 * q^62 + 3514567662 * q^63 - 1840657236 * q^65 + 19323290088 * q^66 + 20641904172 * q^67 - 5240868870 * q^68 - 8235161100 * q^70 - 24 * q^71 - 64729344936 * q^72 - 3449985870 * q^73 - 34306313016 * q^75 + 10512445536 * q^76 + 46076293368 * q^77 - 51672410862 * q^78 + 20602412592 * q^80 + 46901590776 * q^81 - 12506757996 * q^82 + 22786639188 * q^83 - 22949887236 * q^85 - 81567902124 * q^86 + 3763013226 * q^87 + 8846542842 * q^88 + 87014491266 * q^90 + 37012815456 * q^91 - 35376892980 * q^92 + 96817414890 * q^93 - 20594188944 * q^95 + 84921616752 * q^96 - 9492824088 * q^97 - 86078409906 * 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.q.a	$95$	$11$	95.q	95.q	$36$	$1176$	$98$	$60.359$		None		✓	✓	✓	95.11.q.a	$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(-11688\)		$\mathrm{SU}(2)[C_{36}]$