Space of modular forms of level 858, weight 2, and Character 858.bo

• Label: 858.2.bo
• Level: $858$
• Weight: $2$
• Character orbit: 858.bo
• Rep. character: $\chi_{858}(49,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $224$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	858.bo (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 143 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(858, [\chi])\).

	Total	New	Old
Modular forms	1408	224	1184
Cusp forms	1280	224	1056
Eisenstein series	128	0	128

Trace form

224 * q - 28 * q^4 + 28 * q^9 + 32 * q^10 - 60 * q^11 + 28 * q^13 - 8 * q^14 + 24 * q^15 + 28 * q^16 - 4 * q^17 + 24 * q^19 - 4 * q^22 - 24 * q^23 + 80 * q^25 - 20 * q^26 + 12 * q^29 - 8 * q^30 - 12 * q^33 - 16 * q^35 - 28 * q^36 - 8 * q^38 + 8 * q^39 - 16 * q^40 - 72 * q^41 + 64 * q^43 - 36 * q^46 + 8 * q^49 + 64 * q^51 - 4 * q^52 + 56 * q^53 + 20 * q^55 + 16 * q^56 - 12 * q^58 - 84 * q^59 + 40 * q^61 + 12 * q^62 + 56 * q^64 - 40 * q^65 + 32 * q^66 + 72 * q^67 + 4 * q^68 + 28 * q^69 - 84 * q^71 + 8 * q^74 - 8 * q^75 + 24 * q^76 + 88 * q^77 + 40 * q^79 + 28 * q^81 + 8 * q^82 + 120 * q^85 - 8 * q^87 - 16 * q^88 + 72 * q^89 + 16 * q^90 - 4 * q^91 - 8 * q^92 + 48 * q^93 + 24 * q^94 - 112 * q^95 + 156 * q^97 - 96 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(858, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
858.2.bo.a	$858$	$2$	858.bo	143.u	$30$	$112$	$14$	$6.851$		None		✓			858.2.bo.a	$4$	$0$	\(0\)	\(-14\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$
858.2.bo.b	$858$	$2$	858.bo	143.u	$30$	$112$	$14$	$6.851$		None		✓			858.2.bo.b	$4$	$0$	\(0\)	\(14\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(858, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(858, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 2}\)