Space of modular forms of level 336, weight 4, and Character 336.h

• Label: 336.4.h
• Level: $336$
• Weight: $4$
• Character orbit: 336.h
• Rep. character: $\chi_{336}(239,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $256$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(336, [\chi])\).

	Total	New	Old
Modular forms	204	36	168
Cusp forms	180	36	144
Eisenstein series	24	0	24

Trace form

\( 36 q - 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(336, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.4.h.a	$336$	$4$	336.h	12.b	$2$	$12$	$12$	$19.825$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{8}q^{5}-\beta _{1}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots\)
336.4.h.b	$336$	$4$	336.h	12.b	$2$	$24$	$24$	$19.825$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(336, [\chi]) \cong \)