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

• Label: 357.2.u
• Level: $357$
• Weight: $2$
• Character orbit: 357.u
• Rep. character: $\chi_{357}(43,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.u (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	208	80	128
Cusp forms	176	80	96
Eisenstein series	32	0	32

Trace form

80 * q + 16 * q^6 - 128 * q^16 - 16 * q^17 + 16 * q^19 - 32 * q^20 - 16 * q^23 - 16 * q^24 + 48 * q^25 + 32 * q^26 - 16 * q^31 - 80 * q^32 + 16 * q^33 + 16 * q^34 - 16 * q^36 + 32 * q^37 - 32 * q^39 + 80 * q^40 + 16 * q^41 + 64 * q^44 + 16 * q^45 - 64 * q^52 + 16 * q^54 + 32 * q^57 - 64 * q^58 - 64 * q^59 + 16 * q^60 + 48 * q^61 + 80 * q^62 - 80 * q^65 + 32 * q^66 + 96 * q^68 - 16 * q^69 - 16 * q^70 - 64 * q^71 - 80 * q^73 - 64 * q^74 - 32 * q^75 + 64 * q^76 - 32 * q^77 - 64 * q^79 - 112 * q^80 - 48 * q^83 - 48 * q^84 - 32 * q^85 - 64 * q^86 - 112 * q^88 + 16 * q^91 + 224 * q^92 + 16 * q^93 + 160 * q^94 - 32 * q^95 - 64 * q^96 - 64 * q^97

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.u.a	$357$	$2$	357.u	17.d	$8$	$32$	$8$	$2.851$		None		✓			357.2.u.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
357.2.u.b	$357$	$2$	357.u	17.d	$8$	$48$	$12$	$2.851$		None		✓	✓		357.2.u.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(357, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)