Space of modular forms of level 348, weight 2, and Character 348.i

• Label: 348.2.i
• Level: $348$
• Weight: $2$
• Character orbit: 348.i
• Rep. character: $\chi_{348}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(348, [\chi])\).

	Total	New	Old
Modular forms	128	60	68
Cusp forms	112	60	52
Eisenstein series	16	0	16

Trace form

\( 60 q + 4 q^{2} + 4 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(348, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
348.2.i.a	$348$	$2$	348.i	116.e	$4$	$60$	$30$	$2.779$		None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(348, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(348, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)