Space of modular forms of level 350, weight 4, and Character 350.g

• Label: 350.4.g
• Level: $350$
• Weight: $4$
• Character orbit: 350.g
• Rep. character: $\chi_{350}(293,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(350, [\chi])\).

	Total	New	Old
Modular forms	384	72	312
Cusp forms	336	72	264
Eisenstein series	48	0	48

Trace form

\( 72 q - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
350.4.g.a	$350$	$4$	350.g	35.f	$4$	$16$	$8$	$20.651$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{7}q^{2}+\beta _{2}q^{3}-4\beta _{3}q^{4}-\beta _{9}q^{6}+\cdots\)
350.4.g.b	$350$	$4$	350.g	35.f	$4$	$24$	$12$	$20.651$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$
350.4.g.c	$350$	$4$	350.g	35.f	$4$	$32$	$16$	$20.651$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

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