Space of modular forms of level 334, weight 2, and trivial character

• Label: 334.2.a
• Level: $334$
• Weight: $2$
• Character orbit: 334.a
• Rep. character: $\chi_{334}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $6$
• Sturm bound: $84$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 334 = 2 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	334.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(84\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(334))\).

	Total	New	Old
Modular forms	44	13	31
Cusp forms	41	13	28
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.

\(2\)	\(167\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(4\)
Minus space		\(-\)	\(9\)

Trace form

\( 13 q - q^{2} - 4 q^{3} + 13 q^{4} - 4 q^{5} - 8 q^{7} - q^{8} + 13 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(334))\) 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	167
334.2.a.a	$334$	$2$	334.a	1.a	$1$	$1$	$1$	$2.667$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
334.2.a.b	$334$	$2$	334.a	1.a	$1$	$2$	$2$	$2.667$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
334.2.a.c	$334$	$2$	334.a	1.a	$1$	$2$	$2$	$2.667$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2\beta q^{3}+q^{4}+(1-\beta )q^{5}-2\beta q^{6}+\cdots\)
334.2.a.d	$334$	$2$	334.a	1.a	$1$	$2$	$2$	$2.667$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-3\)	\(-4\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
334.2.a.e	$334$	$2$	334.a	1.a	$1$	$3$	$3$	$2.667$	3.3.469.1	None	✓	$1$	$0$	\(-3\)	\(-1\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
334.2.a.f	$334$	$2$	334.a	1.a	$1$	$3$	$3$	$2.667$	3.3.733.1	None	✓	$1$	$0$	\(3\)	\(1\)	\(-3\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(334))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(334)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 2}\)