Space of modular forms of level 198, weight 2, and Character 198.f

• Label: 198.2.f
• Level: $198$
• Weight: $2$
• Character orbit: 198.f
• Rep. character: $\chi_{198}(37,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $72$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(72\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(198, [\chi])\).

	Total	New	Old
Modular forms	176	20	156
Cusp forms	112	20	92
Eisenstein series	64	0	64

Trace form

20 * q + q^2 - 5 * q^4 - 2 * q^5 + 10 * q^7 + q^8 + 12 * q^10 + 9 * q^11 + 12 * q^13 + 2 * q^14 - 5 * q^16 + 14 * q^17 + 11 * q^19 - 2 * q^20 + q^22 + 4 * q^23 - 35 * q^25 - 18 * q^26 - 10 * q^28 + 2 * q^29 - 22 * q^31 - 4 * q^32 - 14 * q^34 - 40 * q^35 - 18 * q^37 - 22 * q^38 - 8 * q^40 - 18 * q^41 - 26 * q^43 + 4 * q^44 - 12 * q^46 + 20 * q^47 + 23 * q^49 + 35 * q^50 - 18 * q^52 + 16 * q^53 - 44 * q^55 - 8 * q^56 + 22 * q^58 + 7 * q^59 - 16 * q^61 + 14 * q^62 - 5 * q^64 - 8 * q^65 + 6 * q^67 + 14 * q^68 + 20 * q^70 - 4 * q^71 - 18 * q^73 + 34 * q^74 + 6 * q^76 - 14 * q^79 + 8 * q^80 + 33 * q^82 - 9 * q^83 + 18 * q^85 - 5 * q^86 + 11 * q^88 - 6 * q^89 + 84 * q^91 - 26 * q^92 + 4 * q^94 - 42 * q^95 + 53 * q^97 - 36 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(198, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
198.2.f.a	$198$	$2$	198.f	11.c	$5$	$4$	$1$	$1.581$	\(\Q(\zeta_{10})\)	None					66.2.e.b	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
198.2.f.b	$198$	$2$	198.f	11.c	$5$	$4$	$1$	$1.581$	\(\Q(\zeta_{10})\)	None		✓			198.2.f.b	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
198.2.f.c	$198$	$2$	198.f	11.c	$5$	$4$	$1$	$1.581$	\(\Q(\zeta_{10})\)	None					66.2.e.a	$2$	$0$	\(1\)	\(0\)	\(-8\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
198.2.f.d	$198$	$2$	198.f	11.c	$5$	$4$	$1$	$1.581$	\(\Q(\zeta_{10})\)	None		✓			198.2.f.b	$2$	$0$	\(1\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
198.2.f.e	$198$	$2$	198.f	11.c	$5$	$4$	$1$	$1.581$	\(\Q(\zeta_{10})\)	None					22.2.c.a	$2$	$0$	\(1\)	\(0\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(198, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(198, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)