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

• Label: 858.2.bi
• Level: $858$
• Weight: $2$
• Character orbit: 858.bi
• Rep. character: $\chi_{858}(5,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $448$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	858.bi (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 429 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	1408	448	960
Cusp forms	1280	448	832
Eisenstein series	128	0	128

Trace form

448 * q + 16 * q^13 + 24 * q^15 + 112 * q^16 - 16 * q^18 - 16 * q^19 + 48 * q^27 + 16 * q^31 + 64 * q^33 - 16 * q^34 - 24 * q^39 - 64 * q^45 + 24 * q^46 + 24 * q^54 + 24 * q^57 - 16 * q^60 + 48 * q^61 + 88 * q^63 + 48 * q^67 - 16 * q^70 + 24 * q^72 - 16 * q^76 + 64 * q^78 - 208 * q^79 - 208 * q^81 + 80 * q^85 + 16 * q^91 + 128 * q^93 - 192 * q^94 - 128 * q^97 + 64 * q^99

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.bi.a	$858$	$2$	858.bi	429.ai	$20$	$448$	$56$	$6.851$		None		✓	✓	✓	858.2.bi.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

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

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