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

• Label: 1050.2.m
• Level: $1050$
• Weight: $2$
• Character orbit: 1050.m
• Rep. character: $\chi_{1050}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $480$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(480\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	528	48	480
Cusp forms	432	48	384
Eisenstein series	96	0	96

Trace form

\( 48 q - 12 q^{7} + O(q^{10}) \)

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.m.a	$1050$	$2$	1050.m	35.f	$4$	$8$	$4$	$8.384$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+\beta _{3}q^{3}-\beta _{5}q^{4}+\beta _{5}q^{6}+\cdots\)
1050.2.m.b	$1050$	$2$	1050.m	35.f	$4$	$8$	$4$	$8.384$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}-\beta _{3}q^{3}-\beta _{5}q^{4}-\beta _{5}q^{6}+\cdots\)
1050.2.m.c	$1050$	$2$	1050.m	35.f	$4$	$8$	$4$	$8.384$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{24}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{4}-\zeta_{24}^{3}q^{6}+\cdots\)
1050.2.m.d	$1050$	$2$	1050.m	35.f	$4$	$8$	$4$	$8.384$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{24}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{3}q^{4}+\zeta_{24}^{3}q^{6}+\cdots\)
1050.2.m.e	$1050$	$2$	1050.m	35.f	$4$	$8$	$4$	$8.384$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}-\beta _{2}q^{6}+\cdots\)
1050.2.m.f	$1050$	$2$	1050.m	35.f	$4$	$8$	$4$	$8.384$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots\)

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

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