Space of modular forms of level 351, weight 2, and Character 351.l

• Label: 351.2.l
• Level: $351$
• Weight: $2$
• Character orbit: 351.l
• Rep. character: $\chi_{351}(127,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(351, [\chi])\).

	Total	New	Old
Modular forms	96	32	64
Cusp forms	72	24	48
Eisenstein series	24	8	16

Trace form

24 * q - 22 * q^4 - 3 * q^7 - 4 * q^10 - 2 * q^13 + 6 * q^14 + 14 * q^16 - 6 * q^17 - 9 * q^19 + 27 * q^20 + 14 * q^22 - 9 * q^23 + 2 * q^25 - 36 * q^29 - 12 * q^31 + 6 * q^34 + 24 * q^35 - 3 * q^37 - 24 * q^38 + 16 * q^40 + 15 * q^41 - 3 * q^43 - 6 * q^46 - 3 * q^47 + 3 * q^49 - 12 * q^50 - 20 * q^52 + 12 * q^53 - 7 * q^55 + 6 * q^56 + 8 * q^61 - 15 * q^62 - 26 * q^64 + 66 * q^65 - 24 * q^67 + 66 * q^68 - 15 * q^70 + 6 * q^71 + 15 * q^74 + 21 * q^76 - 48 * q^77 + 5 * q^79 - 90 * q^80 + 5 * q^82 - 51 * q^83 - 42 * q^86 + 10 * q^88 + 3 * q^89 + 6 * q^91 + 6 * q^92 + 35 * q^94 - 105 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(351, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
351.2.l.a	$351$	$2$	351.l	117.l	$6$	$2$	$1$	$2.803$	\(\Q(\sqrt{-3}) \)	None					117.2.l.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{2}-q^{4}+(-1-\zeta_{6})q^{5}+\cdots\)
351.2.l.b	$351$	$2$	351.l	117.l	$6$	$22$	$11$	$2.803$		None			✓		117.2.l.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-6\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(351, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(351, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)