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

• Label: 1050.2.u
• Level: $1050$
• Weight: $2$
• Character orbit: 1050.u
• Rep. character: $\chi_{1050}(299,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $480$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(480\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	528	96	432
Cusp forms	432	96	336
Eisenstein series	96	0	96

Trace form

\( 96 q - 48 q^{4} - 12 q^{9} + O(q^{10}) \)

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.u.a	$1050$	$2$	1050.u	105.p	$6$	$4$	$2$	$8.384$	\(\Q(\zeta_{12})\)	None		$4$	$1$	\(-2\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{2}q^{2}+(-1-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1050.2.u.b	$1050$	$2$	1050.u	105.p	$6$	$4$	$2$	$8.384$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
1050.2.u.c	$1050$	$2$	1050.u	105.p	$6$	$4$	$2$	$8.384$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1050.2.u.d	$1050$	$2$	1050.u	105.p	$6$	$4$	$2$	$8.384$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{2}q^{2}+(1+\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1050.2.u.e	$1050$	$2$	1050.u	105.p	$6$	$12$	$6$	$8.384$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-6\)	\(2\)	\(0\)	\(-6\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}-\beta _{8}q^{3}+(-1+\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
1050.2.u.f	$1050$	$2$	1050.u	105.p	$6$	$12$	$6$	$8.384$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-6\)	\(4\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
1050.2.u.g	$1050$	$2$	1050.u	105.p	$6$	$12$	$6$	$8.384$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(6\)	\(-4\)	\(0\)	\(-6\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
1050.2.u.h	$1050$	$2$	1050.u	105.p	$6$	$12$	$6$	$8.384$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(6\)	\(-2\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{2}+\beta _{8}q^{3}+(-1+\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
1050.2.u.i	$1050$	$2$	1050.u	105.p	$6$	$16$	$8$	$8.384$	16.0.\(\cdots\).8	None		$4$	$0$	\(-8\)	\(6\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{12}q^{2}-\beta _{14}q^{3}+(-1-\beta _{12})q^{4}+\cdots\)
1050.2.u.j	$1050$	$2$	1050.u	105.p	$6$	$16$	$8$	$8.384$	16.0.\(\cdots\).8	None		$4$	$0$	\(8\)	\(-6\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{12}q^{2}+\beta _{14}q^{3}+(-1-\beta _{12})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)