Space of modular forms of level 298, weight 2, and trivial character

• Label: 298.2.a
• Level: $298$
• Weight: $2$
• Character orbit: 298.a
• Rep. character: $\chi_{298}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $75$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 298 = 2 \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	298.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(75\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(298))\).

	Total	New	Old
Modular forms	39	12	27
Cusp forms	36	12	24
Eisenstein series	3	0	3

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

\(2\)	\(149\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(5\)
Minus space		\(-\)	\(7\)

Trace form

\( 12 q - 4 q^{3} + 12 q^{4} + 2 q^{5} + 2 q^{6} + 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(298))\) 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	149
298.2.a.a	$298$	$2$	298.a	1.a	$1$	$1$	$1$	$2.380$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
298.2.a.b	$298$	$2$	298.a	1.a	$1$	$1$	$1$	$2.380$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}-2q^{7}+\cdots\)
298.2.a.c	$298$	$2$	298.a	1.a	$1$	$2$	$2$	$2.380$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
298.2.a.d	$298$	$2$	298.a	1.a	$1$	$3$	$3$	$2.380$	3.3.169.1	None	✓	$1$	$1$	\(-3\)	\(-5\)	\(1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-2+\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots\)
298.2.a.e	$298$	$2$	298.a	1.a	$1$	$5$	$5$	$2.380$	5.5.617176.1	None	✓	$1$	$0$	\(5\)	\(1\)	\(5\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(298))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(298)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 2}\)