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 - 56 * q^11 + 32 * q^14 - 192 * q^16 - 156 * q^19 - 12 * q^21 - 192 * q^26 - 192 * q^29 - 24 * q^31 - 576 * q^36 - 36 * q^39 + 112 * q^44 + 16 * q^46 + 244 * q^49 + 48 * q^51 + 128 * q^56 - 1008 * q^59 + 204 * q^61 - 768 * q^64 - 32 * q^71 + 512 * q^74 - 136 * q^79 - 432 * q^81 - 48 * q^84 - 368 * q^86 + 96 * q^89 - 1612 * q^91 - 576 * q^94 + 336 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1050.3.q.a	$1050$	$3$	1050.q	35.i	$6$	$8$	$4$	$28.610$	\(\Q(\zeta_{24})\)	None					42.3.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_{5} q^{2}+(-2\beta_{3}+\beta_1)q^{3}+(-2\beta_{2}+2)q^{4}+\cdots\)
1050.3.q.b	$1050$	$3$	1050.q	35.i	$6$	$16$	$8$	$28.610$	16.0.\(\cdots\).1	None		✓			1050.3.p.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(2+2\beta _{3}+\cdots)q^{4}+\cdots\)
1050.3.q.c	$1050$	$3$	1050.q	35.i	$6$	$16$	$8$	$28.610$	16.0.\(\cdots\).1	None					210.3.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{13}q^{2}+(\beta _{1}+2\beta _{8})q^{3}-2\beta _{6}q^{4}+\cdots\)
1050.3.q.d	$1050$	$3$	1050.q	35.i	$6$	$24$	$12$	$28.610$		None		✓			1050.3.p.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1050.3.q.e	$1050$	$3$	1050.q	35.i	$6$	$32$	$16$	$28.610$		None			✓		210.3.o.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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