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

• Label: 95.11.n
• Level: $95$
• Weight: $11$
• Character orbit: 95.n
• Rep. character: $\chi_{95}(21,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $396$
• Newform subspaces: $1$
• Sturm bound: $110$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.n (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{18})\)
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	612	396	216
Cusp forms	588	396	192
Eisenstein series	24	0	24

Trace form

396 * q + 132 * q^3 - 1830 * q^4 + 3066 * q^6 - 95436 * q^9 - 93750 * q^10 + 2985984 * q^12 - 2110026 * q^13 + 1224960 * q^14 - 6809430 * q^16 + 532380 * q^17 - 7959948 * q^19 - 9580518 * q^21 - 31211136 * q^22 - 13532700 * q^23 + 21417984 * q^24 - 159720 * q^26 - 183408156 * q^27 + 144654336 * q^28 - 140983194 * q^29 - 119625000 * q^30 + 122776776 * q^31 + 393148500 * q^32 - 359004150 * q^33 - 578370492 * q^34 - 59812500 * q^35 - 640932912 * q^36 + 503327622 * q^38 + 1302975096 * q^39 - 96000000 * q^40 - 1194423528 * q^41 - 3390185778 * q^42 - 670104582 * q^43 + 2150443914 * q^44 + 3016431090 * q^46 - 151507770 * q^47 + 364629606 * q^48 - 8225668806 * q^49 + 3009006312 * q^51 - 2363609406 * q^52 - 4515798744 * q^53 - 9311985042 * q^54 + 952636938 * q^57 + 4039140864 * q^58 + 5041664862 * q^59 - 2779312500 * q^60 + 5128963260 * q^61 - 4033454760 * q^62 - 12114094326 * q^63 + 11990621196 * q^64 - 3916687500 * q^65 - 1806217476 * q^66 + 6379678362 * q^67 + 18479546670 * q^68 + 14567082498 * q^69 - 1621125000 * q^70 - 1788156144 * q^71 - 16923552852 * q^72 - 26786299530 * q^73 + 15012453948 * q^74 + 18346685868 * q^76 + 6003303804 * q^77 + 69668310660 * q^78 - 9538312266 * q^79 + 5565750000 * q^80 + 2012656020 * q^81 + 30701977302 * q^82 - 21873008760 * q^83 - 51655671540 * q^84 - 14398500000 * q^85 - 14081837694 * q^86 - 17926323216 * q^87 + 110136441168 * q^88 + 77332013844 * q^89 + 18945093750 * q^90 - 85587979728 * q^91 + 50548839756 * q^92 - 13898204208 * q^93 + 262589518236 * q^96 + 29548158042 * q^97 - 235808629536 * q^98 - 91369111794 * q^99

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.n.a	$95$	$11$	95.n	19.f	$18$	$396$	$66$	$60.359$		None		✓	✓	✓	95.11.n.a	$2$	$0$	\(0\)	\(132\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{11}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(95, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)