Space of modular forms of level 1050, weight 2, and Character 1050.g

• Label: 1050.2.g
• Level: $1050$
• Weight: $2$
• Character orbit: 1050.g
• Rep. character: $\chi_{1050}(799,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $10$
• Sturm bound: $480$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(480\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1050, [\chi])\).

	Total	New	Old
Modular forms	264	20	244
Cusp forms	216	20	196
Eisenstein series	48	0	48

Trace form

\( 20 q - 20 q^{4} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1050.2.g.a	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{7}-iq^{8}+\cdots\)
1050.2.g.b	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.c	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
1050.2.g.d	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.e	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{7}-iq^{8}+\cdots\)
1050.2.g.f	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.g	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
1050.2.g.h	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.i	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
1050.2.g.j	$1050$	$2$	1050.g	5.b	$2$	$2$	$2$	$8.384$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)