Space of modular forms of level 336, weight 2, and Character 336.w

• Label: 336.2.w
• Level: $336$
• Weight: $2$
• Character orbit: 336.w
• Rep. character: $\chi_{336}(85,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

	Total	New	Old
Modular forms	136	48	88
Cusp forms	120	48	72
Eisenstein series	16	0	16

Trace form

48 * q + 4 * q^4 - 8 * q^10 + 8 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^15 + 4 * q^16 - 4 * q^18 + 16 * q^19 - 20 * q^22 - 8 * q^24 - 40 * q^26 + 16 * q^29 + 16 * q^30 - 32 * q^34 + 8 * q^36 + 16 * q^37 + 56 * q^38 - 40 * q^40 + 24 * q^43 + 52 * q^44 - 24 * q^46 - 48 * q^49 + 68 * q^50 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 8 * q^54 - 28 * q^56 + 4 * q^58 - 24 * q^60 - 32 * q^61 - 48 * q^62 - 8 * q^63 + 28 * q^64 + 32 * q^65 - 8 * q^67 - 104 * q^68 - 32 * q^69 - 24 * q^70 + 4 * q^72 + 12 * q^74 - 32 * q^75 - 40 * q^76 - 16 * q^77 + 24 * q^78 + 48 * q^79 - 80 * q^80 - 48 * q^81 - 40 * q^82 + 80 * q^83 + 32 * q^85 - 60 * q^86 + 20 * q^88 + 16 * q^90 + 48 * q^92 - 40 * q^94 + 40 * q^96 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.2.w.a	$336$	$2$	336.w	16.e	$4$	$20$	$10$	$2.683$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			336.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}-\beta _{7}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6}-\beta _{16}+\cdots)q^{4}+\cdots\)
336.2.w.b	$336$	$2$	336.w	16.e	$4$	$28$	$14$	$2.683$		None		✓	✓		336.2.w.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)