Space of modular forms of level 98, weight 2, and trivial character

• Label: 98.2.a
• Level: $98$
• Weight: $2$
• Character orbit: 98.a
• Rep. character: $\chi_{98}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(98))\).

	Total	New	Old
Modular forms	22	3	19
Cusp forms	7	3	4
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.

\(2\)	\(7\)	Fricke	Dim
\(+\)	\(-\)	$-$	\(1\)
\(-\)	\(+\)	$-$	\(2\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(3\)

Trace form

\( 3 q + q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{6} + q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(98))\) 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	7
98.2.a.a	$98$	$2$	98.a	1.a	$1$	$1$	$1$	$0.783$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
98.2.a.b	$98$	$2$	98.a	1.a	$1$	$2$	$2$	$0.783$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(98))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(98)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)