Space of modular forms of level 1050, weight 4, and Character 1050.g

• Label: 1050.4.g
• Level: $1050$
• Weight: $4$
• Character orbit: 1050.g
• Rep. character: $\chi_{1050}(799,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $22$
• Sturm bound: $960$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1050.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(960\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1050, [\chi])\).

	Total	New	Old
Modular forms	744	52	692
Cusp forms	696	52	644
Eisenstein series	48	0	48

Trace form

\( 52 q - 208 q^{4} - 468 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1050, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1050.4.g.a	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-3iq^{3}-4q^{4}-6q^{6}-7iq^{7}+\cdots\)
1050.4.g.b	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}-7iq^{7}+\cdots\)
1050.4.g.c	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}-7iq^{7}+\cdots\)
1050.4.g.d	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}-7iq^{7}+\cdots\)
1050.4.g.e	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-3iq^{3}-4q^{4}-6q^{6}-7iq^{7}+\cdots\)
1050.4.g.f	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-3iq^{3}-4q^{4}-6q^{6}+7iq^{7}+\cdots\)
1050.4.g.g	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}+7iq^{7}+\cdots\)
1050.4.g.h	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}-3iq^{3}-4q^{4}-6q^{6}-7iq^{7}+\cdots\)
1050.4.g.i	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}+7iq^{7}+\cdots\)
1050.4.g.j	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}-7iq^{7}+\cdots\)
1050.4.g.k	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+7iq^{7}+\cdots\)
1050.4.g.l	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}-7iq^{7}+\cdots\)
1050.4.g.m	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}+3iq^{3}-4q^{4}+6q^{6}-7iq^{7}+\cdots\)
1050.4.g.n	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}-7iq^{7}+\cdots\)
1050.4.g.o	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}+3iq^{3}-4q^{4}+6q^{6}+7iq^{7}+\cdots\)
1050.4.g.p	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}+3iq^{3}-4q^{4}+6q^{6}+7iq^{7}+\cdots\)
1050.4.g.q	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}+3iq^{3}-4q^{4}+6q^{6}+7iq^{7}+\cdots\)
1050.4.g.r	$1050$	$4$	1050.g	5.b	$2$	$2$	$2$	$61.952$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{2}+3iq^{3}-4q^{4}+6q^{6}+7iq^{7}+\cdots\)
1050.4.g.s	$1050$	$4$	1050.g	5.b	$2$	$4$	$4$	$61.952$	\(\Q(i, \sqrt{1129})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{2}q^{2}-3\beta _{2}q^{3}-4q^{4}-6q^{6}+\cdots\)
1050.4.g.t	$1050$	$4$	1050.g	5.b	$2$	$4$	$4$	$61.952$	\(\Q(i, \sqrt{6001})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+3\beta _{2}q^{3}-4q^{4}-6q^{6}+\cdots\)
1050.4.g.u	$1050$	$4$	1050.g	5.b	$2$	$4$	$4$	$61.952$	\(\Q(i, \sqrt{8761})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{2}q^{2}+3\beta _{2}q^{3}-4q^{4}+6q^{6}+\cdots\)
1050.4.g.v	$1050$	$4$	1050.g	5.b	$2$	$4$	$4$	$61.952$	\(\Q(i, \sqrt{106})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{2}-3\beta _{1}q^{3}-4q^{4}+6q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)