Space of modular forms of level 840, weight 2, and Character 840.j

• Label: 840.2.j
• Level: $840$
• Weight: $2$
• Character orbit: 840.j
• Rep. character: $\chi_{840}(589,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).

	Total	New	Old
Modular forms	200	72	128
Cusp forms	184	72	112
Eisenstein series	16	0	16

Trace form

72 * q - 4 * q^4 + 4 * q^6 + 72 * q^9 + 8 * q^10 - 20 * q^16 + 20 * q^20 + 4 * q^24 - 8 * q^25 + 40 * q^26 - 8 * q^30 + 16 * q^31 - 4 * q^36 + 32 * q^39 - 40 * q^40 + 16 * q^41 - 80 * q^44 + 24 * q^46 - 72 * q^49 - 48 * q^50 + 4 * q^54 + 32 * q^55 - 24 * q^56 + 12 * q^60 + 44 * q^64 + 48 * q^65 - 16 * q^66 + 12 * q^70 - 8 * q^74 - 72 * q^76 - 64 * q^79 - 68 * q^80 + 72 * q^81 - 88 * q^86 + 80 * q^89 + 8 * q^90 + 32 * q^94 - 80 * q^95 + 44 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(840, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
840.2.j.a	$840$	$2$	840.j	40.f	$2$	$2$	$2$	$6.707$	\(\Q(\sqrt{-1}) \)	None		✓			840.2.j.a	$2$	$1$	\(-2\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i-1)q^{2}-q^{3}+2 i q^{4}+(i-2)q^{5}+\cdots\)
840.2.j.b	$840$	$2$	840.j	40.f	$2$	$2$	$2$	$6.707$	\(\Q(\sqrt{-1}) \)	None		✓			840.2.j.b	$2$	$1$	\(-2\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}+q^{3}-2 i q^{4}+(-i-2)q^{5}+\cdots\)
840.2.j.c	$840$	$2$	840.j	40.f	$2$	$2$	$2$	$6.707$	\(\Q(\sqrt{-1}) \)	None		✓			840.2.j.b	$2$	$0$	\(2\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}-q^{3}+2 i q^{4}+(i+2)q^{5}+\cdots\)
840.2.j.d	$840$	$2$	840.j	40.f	$2$	$2$	$2$	$6.707$	\(\Q(\sqrt{-1}) \)	None		✓			840.2.j.a	$2$	$0$	\(2\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}+q^{3}+2 i q^{4}+(i+2)q^{5}+\cdots\)
840.2.j.e	$840$	$2$	840.j	40.f	$2$	$32$	$32$	$6.707$		None		✓			840.2.j.e	$2$	$0$	\(-2\)	\(-32\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
840.2.j.f	$840$	$2$	840.j	40.f	$2$	$32$	$32$	$6.707$		None		✓			840.2.j.e	$2$	$0$	\(2\)	\(32\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)