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

• Label: 348.2.h
• Level: $348$
• Weight: $2$
• Character orbit: 348.h
• Rep. character: $\chi_{348}(289,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	66	6	60
Cusp forms	54	6	48
Eisenstein series	12	0	12

Trace form

\( 6 q + 4 q^{7} - 6 q^{9} + O(q^{10}) \)

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.h.a	$348$	$2$	348.h	29.b	$2$	$2$	$2$	$2.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-2q^{5}-3q^{7}-q^{9}-3iq^{11}+\cdots\)
348.2.h.b	$348$	$2$	348.h	29.b	$2$	$2$	$2$	$2.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-2q^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots\)
348.2.h.c	$348$	$2$	348.h	29.b	$2$	$2$	$2$	$2.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4q^{5}+q^{7}-q^{9}-5iq^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(348, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 2}\)