Space of modular forms of level 351, weight 3, and Character 351.n

• Label: 351.3.n
• Level: $351$
• Weight: $3$
• Character orbit: 351.n
• Rep. character: $\chi_{351}(116,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $52$
• Newform subspaces: $1$
• Sturm bound: $126$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	351.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(126\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(351, [\chi])\).

	Total	New	Old
Modular forms	180	60	120
Cusp forms	156	52	104
Eisenstein series	24	8	16

Trace form

52 * q - 50 * q^4 + 8 * q^10 - 6 * q^13 + 6 * q^14 - 90 * q^16 + 14 * q^22 - 138 * q^23 - 92 * q^25 - 48 * q^29 - 324 * q^38 - 68 * q^40 + 62 * q^43 + 70 * q^49 - 4 * q^52 + 92 * q^55 + 276 * q^56 + 12 * q^61 + 12 * q^64 + 588 * q^65 + 144 * q^68 - 342 * q^74 + 510 * q^77 - 24 * q^79 - 292 * q^82 - 62 * q^88 + 264 * q^91 + 396 * q^92 - 160 * q^94 - 504 * q^95

Decomposition of \(S_{3}^{\mathrm{new}}(351, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
351.3.n.a	$351$	$3$	351.n	117.n	$6$	$52$	$26$	$9.564$		None			✓	✓	117.3.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(351, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(351, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)