Space of modular forms of level 338, weight 2, and Character 338.h

• Label: 338.2.h
• Level: $338$
• Weight: $2$
• Character orbit: 338.h
• Rep. character: $\chi_{338}(25,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $192$
• Newform subspaces: $1$
• Sturm bound: $91$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.h (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(91\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(338, [\chi])\).

	Total	New	Old
Modular forms	576	192	384
Cusp forms	528	192	336
Eisenstein series	48	0	48

Trace form

\( 192 q + 2 q^{3} + 16 q^{4} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(338, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
338.2.h.a	$338$	$2$	338.h	169.h	$26$	$192$	$16$	$2.699$		None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{26}]$

Decomposition of \(S_{2}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(338, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)