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

• Label: 351.2.h
• Level: $351$
• Weight: $2$
• Character orbit: 351.h
• Rep. character: $\chi_{351}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

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 + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * 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.h.a	$351$	$2$	351.h	117.h	$3$	$24$	$12$	$2.803$		None			✓	✓	117.2.f.a	$2$	$0$	\(2\)	\(0\)	\(2\)	\(3\)		$\mathrm{SU}(2)[C_{3}]$

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

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