Space of modular forms of level 570, weight 2, and Character 570.bb

• Label: 570.2.bb
• Level: $570$
• Weight: $2$
• Character orbit: 570.bb
• Rep. character: $\chi_{570}(41,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $168$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(570, [\chi])\).

	Total	New	Old
Modular forms	768	168	600
Cusp forms	672	168	504
Eisenstein series	96	0	96

Trace form

168 * q - 6 * q^3 - 6 * q^6 + 6 * q^9 + 48 * q^13 - 24 * q^19 + 72 * q^22 - 6 * q^24 + 18 * q^27 - 24 * q^28 + 30 * q^33 + 24 * q^34 + 6 * q^36 + 24 * q^39 + 48 * q^43 - 12 * q^48 - 108 * q^49 + 42 * q^51 + 24 * q^52 - 72 * q^54 - 156 * q^57 - 48 * q^58 - 96 * q^61 - 96 * q^63 - 84 * q^64 + 30 * q^66 + 12 * q^67 - 108 * q^69 - 12 * q^72 + 168 * q^73 + 36 * q^78 - 24 * q^79 + 78 * q^81 - 12 * q^82 + 12 * q^87 - 24 * q^90 + 48 * q^91 - 84 * q^97 + 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(570, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
570.2.bb.a	$570$	$2$	570.bb	57.j	$18$	$84$	$14$	$4.551$		None		✓			570.2.bb.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
570.2.bb.b	$570$	$2$	570.bb	57.j	$18$	$84$	$14$	$4.551$		None		✓			570.2.bb.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(570, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)