Space of modular forms of level 1050, weight 3, and Character 1050.q

• Label: 1050.3.q
• Level: $1050$
• Weight: $3$
• Character orbit: 1050.q
• Rep. character: $\chi_{1050}(199,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $720$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(720\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1050, [\chi])\).

	Total	New	Old
Modular forms	1008	96	912
Cusp forms	912	96	816
Eisenstein series	96	0	96

Trace form

\( 96 q + 96 q^{4} - 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1050, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1050.3.q.a	$1050$	$3$	1050.q	35.i	$6$	$8$	$4$	$28.610$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{24}^{5}q^{2}+(\zeta_{24}-2\zeta_{24}^{3})q^{3}+(2+\cdots)q^{4}+\cdots\)
1050.3.q.b	$1050$	$3$	1050.q	35.i	$6$	$16$	$8$	$28.610$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(2+2\beta _{3}+\cdots)q^{4}+\cdots\)
1050.3.q.c	$1050$	$3$	1050.q	35.i	$6$	$16$	$8$	$28.610$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{13}q^{2}+(\beta _{1}+2\beta _{8})q^{3}-2\beta _{6}q^{4}+\cdots\)
1050.3.q.d	$1050$	$3$	1050.q	35.i	$6$	$24$	$12$	$28.610$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1050.3.q.e	$1050$	$3$	1050.q	35.i	$6$	$32$	$16$	$28.610$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)