Space of modular forms of level 357, weight 2, and Character 357.bb

• Label: 357.2.bb
• Level: $357$
• Weight: $2$
• Character orbit: 357.bb
• Rep. character: $\chi_{357}(4,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(357, [\chi])\).

	Total	New	Old
Modular forms	208	96	112
Cusp forms	176	96	80
Eisenstein series	32	0	32

Trace form

96 * q + 48 * q^4 + 4 * q^5 + 4 * q^7 + 4 * q^11 - 32 * q^13 + 24 * q^14 - 48 * q^16 + 8 * q^17 + 64 * q^20 - 56 * q^22 - 16 * q^23 - 12 * q^24 + 8 * q^28 + 32 * q^29 + 32 * q^30 - 8 * q^31 - 16 * q^33 + 48 * q^34 - 8 * q^35 - 16 * q^38 - 32 * q^40 + 32 * q^41 - 4 * q^45 - 36 * q^46 - 8 * q^47 + 32 * q^48 - 32 * q^50 - 72 * q^52 - 224 * q^55 + 60 * q^56 - 16 * q^57 - 12 * q^58 + 44 * q^61 - 88 * q^62 + 4 * q^63 - 48 * q^64 + 16 * q^65 + 24 * q^67 + 40 * q^68 + 64 * q^69 - 144 * q^71 - 12 * q^73 - 60 * q^74 - 16 * q^75 - 72 * q^78 - 20 * q^79 - 16 * q^80 + 48 * q^81 + 44 * q^82 - 24 * q^84 - 48 * q^85 - 24 * q^86 - 52 * q^88 - 8 * q^89 + 20 * q^91 - 80 * q^92 + 20 * q^95 + 24 * q^96 + 88 * q^97 - 56 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(357, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
357.2.bb.a	$357$	$2$	357.bb	119.n	$12$	$96$	$24$	$2.851$		None		✓	✓	✓	357.2.bb.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(357, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(357, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)