Space of modular forms of level 98, weight 14, and Character 98.c

• Label: 98.14.c
• Level: $98$
• Weight: $14$
• Character orbit: 98.c
• Rep. character: $\chi_{98}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $88$
• Newform subspaces: $18$
• Sturm bound: $196$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(196\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(98, [\chi])\).

	Total	New	Old
Modular forms	380	88	292
Cusp forms	348	88	260
Eisenstein series	32	0	32

Trace form

88 * q - 180224 * q^4 + 62608 * q^5 - 46592 * q^6 - 25479048 * q^9 + 4236288 * q^10 + 17549436 * q^11 - 55245680 * q^13 + 430947040 * q^15 - 738197504 * q^16 + 173276096 * q^17 + 446870272 * q^18 + 639112600 * q^19 - 512884736 * q^20 + 1860481024 * q^22 - 707667880 * q^23 + 95420416 * q^24 - 10960253148 * q^25 + 1675803136 * q^26 + 13674585456 * q^27 - 25538117984 * q^29 + 1156757760 * q^30 - 7620869816 * q^31 - 8347025624 * q^33 - 20145914880 * q^34 + 208724361216 * q^36 - 25277013872 * q^37 + 13292735232 * q^38 + 107031382520 * q^39 + 17351835648 * q^40 - 200030490576 * q^41 + 424664866184 * q^43 + 71882489856 * q^44 + 224768920936 * q^45 - 63519486208 * q^46 + 84492403800 * q^47 - 255475862528 * q^50 + 271798853756 * q^51 + 113143152640 * q^52 + 27483564720 * q^53 - 228393530624 * q^54 - 876549420096 * q^55 + 763117936488 * q^57 + 461482996736 * q^58 + 1060437579040 * q^59 - 882579537920 * q^60 + 302092281064 * q^61 - 589655209472 * q^62 + 6047313952768 * q^64 + 1398345557224 * q^65 + 2695993323520 * q^66 + 896663713392 * q^67 + 709738889216 * q^68 - 9547459848416 * q^69 + 3853602549584 * q^71 + 1830380634112 * q^72 + 6459088113352 * q^73 + 1126781095936 * q^74 + 3701297994800 * q^75 - 5235610419200 * q^76 + 11987616305152 * q^78 + 14309911029704 * q^79 + 1050387939328 * q^80 - 26144836783840 * q^81 + 872746581504 * q^82 - 3647678607328 * q^83 - 4533958394176 * q^85 + 721370500864 * q^86 + 14980266985544 * q^87 - 3810265137152 * q^88 - 1552477239432 * q^89 - 1899518028800 * q^90 + 5797215272960 * q^92 + 5550450039040 * q^93 + 5005439894784 * q^94 - 25442997242440 * q^95 + 390842023936 * q^96 - 9790396414064 * q^97 + 32870844990232 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(98, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.14.c.a	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					2.14.a.b	$2$	$0$	\(-64\)	\(-1236\)	\(57450\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{6}\zeta_{6}q^{2}+(-1236+1236\zeta_{6})q^{3}+\cdots\)
98.14.c.b	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					14.14.a.b	$2$	$0$	\(-64\)	\(-1026\)	\(4320\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{6}\zeta_{6}q^{2}+(-1026+1026\zeta_{6})q^{3}+\cdots\)
98.14.c.c	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					14.14.a.b	$2$	$0$	\(-64\)	\(1026\)	\(-4320\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{6}\zeta_{6}q^{2}+(1026-1026\zeta_{6})q^{3}+\cdots\)
98.14.c.d	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					2.14.a.b	$2$	$0$	\(-64\)	\(1236\)	\(-57450\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{6}\zeta_{6}q^{2}+(1236-1236\zeta_{6})q^{3}+\cdots\)
98.14.c.e	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					2.14.a.a	$2$	$0$	\(64\)	\(-1836\)	\(3990\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{6}\zeta_{6}q^{2}+(-1836+1836\zeta_{6})q^{3}+\cdots\)
98.14.c.f	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					14.14.a.a	$2$	$0$	\(64\)	\(-1626\)	\(36400\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{6}\zeta_{6}q^{2}+(-1626+1626\zeta_{6})q^{3}+\cdots\)
98.14.c.g	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					14.14.a.a	$2$	$0$	\(64\)	\(1626\)	\(-36400\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{6}\zeta_{6}q^{2}+(1626-1626\zeta_{6})q^{3}+\cdots\)
98.14.c.h	$98$	$14$	98.c	7.c	$3$	$2$	$1$	$105.086$	\(\Q(\sqrt{-3}) \)	None					2.14.a.a	$2$	$0$	\(64\)	\(1836\)	\(-3990\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{6}\zeta_{6}q^{2}+(1836-1836\zeta_{6})q^{3}+\cdots\)
98.14.c.i	$98$	$14$	98.c	7.c	$3$	$4$	$2$	$105.086$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None					14.14.a.d	$2$	$0$	\(-128\)	\(-1106\)	\(-75530\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{6}\beta _{1}q^{2}+(-553+553\beta _{1}-5\beta _{2}+\cdots)q^{3}+\cdots\)
98.14.c.j	$98$	$14$	98.c	7.c	$3$	$4$	$2$	$105.086$	\(\Q(\sqrt{-3}, \sqrt{373})\)	None		✓			98.14.a.g	$4$	$0$	\(-128\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{6}+2^{6}\beta _{1})q^{2}-3\beta _{2}q^{3}-2^{12}\beta _{1}q^{4}+\cdots\)
98.14.c.k	$98$	$14$	98.c	7.c	$3$	$4$	$2$	$105.086$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None					14.14.a.d	$2$	$0$	\(-128\)	\(1106\)	\(75530\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{6}\beta _{1}q^{2}+(553-553\beta _{1}+5\beta _{2}+\cdots)q^{3}+\cdots\)
98.14.c.l	$98$	$14$	98.c	7.c	$3$	$4$	$2$	$105.086$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None					14.14.a.c	$2$	$0$	\(128\)	\(-952\)	\(-32004\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{6}-2^{6}\beta _{1})q^{2}+(-476\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
98.14.c.m	$98$	$14$	98.c	7.c	$3$	$4$	$2$	$105.086$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None					14.14.a.c	$2$	$0$	\(128\)	\(952\)	\(32004\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{6}-2^{6}\beta _{1})q^{2}+(476\beta _{1}+\beta _{2})q^{3}+\cdots\)
98.14.c.n	$98$	$14$	98.c	7.c	$3$	$8$	$4$	$105.086$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					14.14.c.a	$2$	$0$	\(-256\)	\(182\)	\(64400\)	\(0\)	$2^{14}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{6}-2^{6}\beta _{1})q^{2}+(-45\beta _{1}+\beta _{4}+\cdots)q^{3}+\cdots\)
98.14.c.o	$98$	$14$	98.c	7.c	$3$	$8$	$4$	$105.086$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					14.14.c.b	$2$	$0$	\(256\)	\(-182\)	\(-1792\)	\(0\)	$2^{14}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{6}-2^{6}\beta _{1})q^{2}+(-46\beta _{1}-\beta _{2})q^{3}+\cdots\)
98.14.c.p	$98$	$14$	98.c	7.c	$3$	$8$	$4$	$105.086$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			98.14.a.i	$4$	$0$	\(256\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{6}\beta _{1}q^{2}+(-\beta _{2}+\beta _{3})q^{3}+(-2^{12}+\cdots)q^{4}+\cdots\)
98.14.c.q	$98$	$14$	98.c	7.c	$3$	$12$	$6$	$105.086$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			98.14.a.m	$4$	$0$	\(384\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{8}\cdot 7^{12}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{6}-2^{6}\beta _{1})q^{2}+(-\beta _{8}+8\beta _{9})q^{3}+\cdots\)
98.14.c.r	$98$	$14$	98.c	7.c	$3$	$16$	$8$	$105.086$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		98.14.a.n	$4$	$0$	\(-512\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 3^{8}\cdot 7^{24}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{6}\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{12}+2^{12}\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{14}^{\mathrm{old}}(98, [\chi]) \simeq \) \(S_{14}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)