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

• Label: 350.2.g
• Level: $350$
• Weight: $2$
• Character orbit: 350.g
• Rep. character: $\chi_{350}(293,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	144	24	120
Cusp forms	96	24	72
Eisenstein series	48	0	48

Trace form

\( 24 q + 8 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
350.2.g.a	$350$	$2$	350.g	35.f	$4$	$8$	$4$	$2.795$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{3}q^{4}+(\zeta_{16}^{4}+\cdots)q^{6}+\cdots\)
350.2.g.b	$350$	$2$	350.g	35.f	$4$	$16$	$8$	$2.795$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}+\beta _{10}q^{4}+\beta _{15}q^{6}+\cdots\)

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

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