Space of modular forms of level 354, weight 2, and trivial character

• Label: 354.2.a
• Level: $354$
• Weight: $2$
• Character orbit: 354.a
• Rep. character: $\chi_{354}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $8$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(354))\).

	Total	New	Old
Modular forms	64	11	53
Cusp forms	57	11	46
Eisenstein series	7	0	7

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

\(2\)	\(3\)	\(59\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(+\)	\(-\)	$-$	\(1\)
\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	$-$	\(3\)
Plus space			\(+\)	\(2\)
Minus space			\(-\)	\(9\)

Trace form

\( 11 q + q^{2} + q^{3} + 11 q^{4} + 6 q^{5} - q^{6} + 4 q^{7} + q^{8} + 11 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(354))\) 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	59
354.2.a.a	$354$	$2$	354.a	1.a	$1$	$1$	$1$	$2.827$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.b	$354$	$2$	354.a	1.a	$1$	$1$	$1$	$2.827$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
354.2.a.c	$354$	$2$	354.a	1.a	$1$	$1$	$1$	$2.827$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.d	$354$	$2$	354.a	1.a	$1$	$1$	$1$	$2.827$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
354.2.a.e	$354$	$2$	354.a	1.a	$1$	$1$	$1$	$2.827$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
354.2.a.f	$354$	$2$	354.a	1.a	$1$	$1$	$1$	$2.827$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
354.2.a.g	$354$	$2$	354.a	1.a	$1$	$2$	$2$	$2.827$	\(\Q(\sqrt{11}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
354.2.a.h	$354$	$2$	354.a	1.a	$1$	$3$	$3$	$2.827$	3.3.316.1	None	✓	$1$	$0$	\(3\)	\(3\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(354))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(354)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 2}\)