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

• Label: 198.2.b
• Level: $198$
• Weight: $2$
• Character orbit: 198.b
• Rep. character: $\chi_{198}(197,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	44	4	40
Cusp forms	28	4	24
Eisenstein series	16	0	16

Trace form

\( 4 q + 4 q^{4} + 4 q^{16} + 12 q^{22} - 12 q^{25} + 8 q^{31} - 24 q^{34} - 40 q^{37} + 28 q^{49} - 16 q^{55} + 4 q^{64} + 32 q^{67} - 24 q^{82} + 12 q^{88} - 16 q^{97}+O(q^{100}) \)

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.b.a	$198$	$2$	198.b	33.d	$2$	$2$	$2$	$1.581$	\(\Q(\sqrt{-2}) \)	None		✓			198.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
198.2.b.b	$198$	$2$	198.b	33.d	$2$	$2$	$2$	$1.581$	\(\Q(\sqrt{-2}) \)	None		✓			198.2.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+2\beta q^{5}+q^{8}+2\beta q^{10}+\cdots\)

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

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