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

• Label: 338.2.k
• Level: $338$
• Weight: $2$
• Character orbit: 338.k
• Rep. character: $\chi_{338}(17,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $336$
• 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.k (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{78})\)
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	1152	336	816
Cusp forms	1056	336	720
Eisenstein series	96	0	96

Trace form

336 * q - 14 * q^4 + 14 * q^9 - 52 * q^13 + 4 * q^14 + 52 * q^15 + 14 * q^16 + 2 * q^17 + 24 * q^22 + 4 * q^23 + 20 * q^25 + 12 * q^27 - 6 * q^29 - 202 * q^30 + 52 * q^31 - 10 * q^35 - 14 * q^36 - 4 * q^38 - 52 * q^39 + 26 * q^40 - 6 * q^42 + 4 * q^43 - 130 * q^45 - 286 * q^47 + 22 * q^49 + 102 * q^51 + 64 * q^53 - 156 * q^54 - 8 * q^55 + 2 * q^56 + 78 * q^57 + 52 * q^58 - 52 * q^60 - 10 * q^61 + 8 * q^62 - 130 * q^63 + 28 * q^64 + 16 * q^66 - 52 * q^67 - 2 * q^68 + 16 * q^69 - 156 * q^71 - 34 * q^74 + 74 * q^75 + 26 * q^76 - 40 * q^77 + 32 * q^79 - 10 * q^81 + 4 * q^82 - 260 * q^83 - 26 * q^85 - 78 * q^86 + 32 * q^87 + 2 * q^88 - 28 * q^90 + 52 * q^91 + 8 * q^92 + 26 * q^93 + 46 * q^94 - 184 * q^95 - 78 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
338.2.k.a	$338$	$2$	338.k	169.k	$78$	$336$	$14$	$2.699$		None		✓	✓	✓	338.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{78}]$

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

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