Space of modular forms of level 350, weight 2, and Character 350.c

• Label: 350.2.c
• Level: $350$
• Weight: $2$
• Character orbit: 350.c
• Rep. character: $\chi_{350}(99,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(350, [\chi])\).

	Total	New	Old
Modular forms	72	8	64
Cusp forms	48	8	40
Eisenstein series	24	0	24

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
350.2.c.a	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None		✓			350.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{7}+\cdots\)
350.2.c.b	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None					70.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
350.2.c.c	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None		✓			350.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots\)
350.2.c.d	$350$	$2$	350.c	5.b	$2$	$2$	$2$	$2.795$	\(\Q(\sqrt{-1}) \)	None					14.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)