Space of modular forms of level 98, weight 4, and Character 98.c

• Label: 98.4.c
• Level: $98$
• Weight: $4$
• Character orbit: 98.c
• Rep. character: $\chi_{98}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $8$
• Sturm bound: $56$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(56\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(98, [\chi])\).

	Total	New	Old
Modular forms	100	20	80
Cusp forms	68	20	48
Eisenstein series	32	0	32

Trace form

20 * q - 6 * q^3 - 40 * q^4 - 2 * q^5 + 16 * q^6 - 168 * q^9 - 32 * q^10 - 30 * q^11 - 24 * q^12 + 8 * q^13 - 68 * q^15 - 160 * q^16 + 110 * q^17 + 40 * q^18 + 142 * q^19 + 16 * q^20 + 512 * q^22 + 26 * q^23 - 32 * q^24 - 520 * q^25 - 272 * q^26 - 396 * q^27 - 824 * q^29 + 264 * q^30 + 98 * q^31 + 250 * q^33 + 32 * q^34 + 1344 * q^36 + 874 * q^37 - 264 * q^38 + 1604 * q^39 - 128 * q^40 + 1080 * q^41 - 1272 * q^43 - 120 * q^44 - 164 * q^45 + 248 * q^46 + 30 * q^47 + 192 * q^48 - 2720 * q^50 - 250 * q^51 - 16 * q^52 - 150 * q^53 + 184 * q^54 - 1516 * q^55 + 1908 * q^57 + 480 * q^58 + 202 * q^59 + 136 * q^60 - 658 * q^61 + 208 * q^62 + 1280 * q^64 + 1540 * q^65 + 640 * q^66 - 986 * q^67 + 440 * q^68 + 676 * q^69 + 2288 * q^71 + 160 * q^72 - 18 * q^73 - 1280 * q^74 + 296 * q^75 - 1136 * q^76 - 2432 * q^78 - 3078 * q^79 - 32 * q^80 - 1150 * q^81 + 912 * q^82 - 688 * q^83 + 3236 * q^85 - 1256 * q^86 - 676 * q^87 - 1024 * q^88 - 1890 * q^89 - 800 * q^90 - 208 * q^92 - 5210 * q^93 + 744 * q^94 + 1142 * q^95 - 128 * q^96 + 4248 * q^97 - 6560 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(98, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.4.c.a	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	\(\Q(\sqrt{-3}) \)	None					14.4.c.a	$2$	$0$	\(-2\)	\(-5\)	\(-9\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.b	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	\(\Q(\sqrt{-3}) \)	None					14.4.a.b	$2$	$0$	\(-2\)	\(-2\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.c	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	\(\Q(\sqrt{-3}) \)	None					14.4.a.b	$2$	$0$	\(-2\)	\(2\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.d	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	\(\Q(\sqrt{-3}) \)	None					14.4.a.a	$2$	$0$	\(2\)	\(-8\)	\(14\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.e	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	\(\Q(\sqrt{-3}) \)	None					14.4.c.b	$2$	$0$	\(2\)	\(-1\)	\(7\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.f	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	\(\Q(\sqrt{-3}) \)	None					14.4.a.a	$2$	$0$	\(2\)	\(8\)	\(-14\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(8-8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.g	$98$	$4$	98.c	7.c	$3$	$4$	$2$	$5.782$	\(\Q(\sqrt{-3}, \sqrt{22})\)	None		✓			98.4.a.h	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots\)
98.4.c.h	$98$	$4$	98.c	7.c	$3$	$4$	$2$	$5.782$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			98.4.a.g	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+2\beta _{2})q^{2}+(5\beta _{1}+5\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

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