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

• Label: 570.2.f
• Level: $570$
• Weight: $2$
• Character orbit: 570.f
• Rep. character: $\chi_{570}(341,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	128	24	104
Cusp forms	112	24	88
Eisenstein series	16	0	16

Trace form

24 * q + 24 * q^4 + 4 * q^6 + 24 * q^7 - 4 * q^9 + 24 * q^16 + 24 * q^19 + 4 * q^24 - 24 * q^25 + 24 * q^28 - 4 * q^36 + 4 * q^39 + 12 * q^42 - 16 * q^43 - 16 * q^45 - 8 * q^54 - 4 * q^57 - 24 * q^58 + 64 * q^61 - 84 * q^63 + 24 * q^64 - 16 * q^66 - 56 * q^73 + 24 * q^76 + 12 * q^81 + 36 * q^87 - 16 * q^93 + 4 * q^96 - 64 * 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.f.a	$570$	$2$	570.f	57.d	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		✓			570.2.f.a	$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(-\beta_{2}-1)q^{3}+q^{4}+\beta_1 q^{5}+\cdots\)
570.2.f.b	$570$	$2$	570.f	57.d	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		✓			570.2.f.a	$2$	$0$	\(4\)	\(4\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta_{2}+1)q^{3}+q^{4}+\beta_1 q^{5}+\cdots\)
570.2.f.c	$570$	$2$	570.f	57.d	$2$	$8$	$8$	$4.551$	8.0.7278137344.1	None		✓			570.2.f.c	$2$	$0$	\(-8\)	\(2\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.f.d	$570$	$2$	570.f	57.d	$2$	$8$	$8$	$4.551$	8.0.7278137344.1	None		✓			570.2.f.c	$2$	$0$	\(8\)	\(-2\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)

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

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