Space of modular forms of level 198, weight 2, and trivial character

• Label: 198.2.a
• Level: $198$
• Weight: $2$
• Character orbit: 198.a
• Rep. character: $\chi_{198}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $5$
• Sturm bound: $72$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(72\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(198))\).

	Total	New	Old
Modular forms	44	5	39
Cusp forms	29	5	24
Eisenstein series	15	0	15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(-\)	$-$	\(1\)
\(+\)	\(-\)	\(+\)	$-$	\(1\)
\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(-\)	\(+\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	\(-\)	$-$	\(1\)
Plus space			\(+\)	\(1\)
Minus space			\(-\)	\(4\)

Trace form

\( 5 q - q^{2} + 5 q^{4} + 2 q^{5} - q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(198))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	11
198.2.a.a	$198$	$2$	198.a	1.a	$1$	$1$	$1$	$1.581$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-4q^{7}-q^{8}+2q^{10}+\cdots\)
198.2.a.b	$198$	$2$	198.a	1.a	$1$	$1$	$1$	$1.581$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}+q^{11}+2q^{13}+\cdots\)
198.2.a.c	$198$	$2$	198.a	1.a	$1$	$1$	$1$	$1.581$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-2q^{7}-q^{8}-4q^{10}+\cdots\)
198.2.a.d	$198$	$2$	198.a	1.a	$1$	$1$	$1$	$1.581$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{11}+2q^{13}+\cdots\)
198.2.a.e	$198$	$2$	198.a	1.a	$1$	$1$	$1$	$1.581$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}+q^{11}-4q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(198))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(198)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)