Space of modular forms of level 1428, weight 2, and Character 1428.bo

• Label: 1428.2.bo
• Level: $1428$
• Weight: $2$
• Character orbit: 1428.bo
• Rep. character: $\chi_{1428}(253,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.bo (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

	Total	New	Old
Modular forms	1200	64	1136
Cusp forms	1104	64	1040
Eisenstein series	96	0	96

Trace form

64 * q - 16 * q^17 - 16 * q^19 - 16 * q^23 + 48 * q^29 + 48 * q^31 + 16 * q^33 + 32 * q^39 + 32 * q^41 - 32 * q^43 + 16 * q^53 + 32 * q^57 + 32 * q^59 - 16 * q^61 + 32 * q^65 - 16 * q^69 + 32 * q^71 + 32 * q^73 - 32 * q^75 - 32 * q^77 - 32 * q^79 - 48 * q^83 + 16 * q^85 - 16 * q^91 - 48 * q^93 - 32 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1428.2.bo.a	$1428$	$2$	1428.bo	17.d	$8$	$24$	$6$	$11.403$		None		✓			1428.2.bo.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
1428.2.bo.b	$1428$	$2$	1428.bo	17.d	$8$	$40$	$10$	$11.403$		None		✓	✓		1428.2.bo.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(714, [\chi])\)\(^{\oplus 2}\)