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

• Label: 348.2.b
• Level: $348$
• Weight: $2$
• Character orbit: 348.b
• Rep. character: $\chi_{348}(347,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 348 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	64	64	0
Cusp forms	56	56	0
Eisenstein series	8	8	0

Trace form

\( 56 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + O(q^{10}) \)

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.b.a	$348$	$2$	348.b	348.b	$2$	$8$	$8$	$2.779$	8.0.12960000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
348.2.b.b	$348$	$2$	348.b	348.b	$2$	$12$	$12$	$2.779$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	\(\Q(\sqrt{-29}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{2}-\beta _{11}q^{3}-2q^{4}+\beta _{9}q^{5}+\cdots\)
348.2.b.c	$348$	$2$	348.b	348.b	$2$	$12$	$12$	$2.779$	12.0.\(\cdots\).3	\(\Q(\sqrt{-87}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{6}q^{2}+\beta _{4}q^{3}+\beta _{5}q^{4}-\beta _{3}q^{6}+\cdots\)
348.2.b.d	$348$	$2$	348.b	348.b	$2$	$24$	$24$	$2.779$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$