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

• Label: 570.2.d
• Level: $570$
• Weight: $2$
• Character orbit: 570.d
• Rep. character: $\chi_{570}(229,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	128	16	112
Cusp forms	112	16	96
Eisenstein series	16	0	16

Trace form

16 * q - 16 * q^4 + 4 * q^5 - 4 * q^6 - 16 * q^9 + 4 * q^10 - 8 * q^11 + 4 * q^15 + 16 * q^16 + 4 * q^19 - 4 * q^20 + 4 * q^24 + 16 * q^26 - 32 * q^29 + 16 * q^31 - 24 * q^34 + 24 * q^35 + 16 * q^36 - 8 * q^39 - 4 * q^40 - 16 * q^41 + 8 * q^44 - 4 * q^45 + 8 * q^46 - 16 * q^49 - 16 * q^50 + 16 * q^51 + 4 * q^54 + 16 * q^55 - 32 * q^59 - 4 * q^60 + 16 * q^61 - 16 * q^64 + 32 * q^65 - 8 * q^66 - 16 * q^69 + 40 * q^70 + 32 * q^71 + 16 * q^74 - 4 * q^76 + 4 * q^80 + 16 * q^81 - 8 * q^85 - 32 * q^86 - 48 * q^89 - 4 * q^90 - 112 * q^91 - 24 * q^94 + 4 * q^95 - 4 * q^96 + 8 * 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.d.a	$570$	$2$	570.d	5.b	$2$	$2$	$2$	$4.551$	\(\Q(\sqrt{-1}) \)	None		✓			570.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots\)
570.2.d.b	$570$	$2$	570.d	5.b	$2$	$2$	$2$	$4.551$	\(\Q(\sqrt{-1}) \)	None		✓			570.2.d.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}+(i+2)q^{5}+\cdots\)
570.2.d.c	$570$	$2$	570.d	5.b	$2$	$6$	$6$	$4.551$	6.0.350464.1	None		✓			570.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\)
570.2.d.d	$570$	$2$	570.d	5.b	$2$	$6$	$6$	$4.551$	6.0.350464.1	None		✓			570.2.d.d	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(570, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)