Space of modular forms of level 2100, weight 2, and Character 2100.x

• Label: 2100.2.x
• Level: $2100$
• Weight: $2$
• Character orbit: 2100.x
• Rep. character: $\chi_{2100}(1357,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $960$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

	Total	New	Old
Modular forms	1032	48	984
Cusp forms	888	48	840
Eisenstein series	144	0	144

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2100.2.x.a	$2100$	$2$	2100.x	35.f	$4$	$8$	$4$	$16.769$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{24}^{5}q^{3}+(2\zeta_{24}+\zeta_{24}^{7})q^{7}-\zeta_{24}^{3}q^{9}+\cdots\)
2100.2.x.b	$2100$	$2$	2100.x	35.f	$4$	$8$	$4$	$16.769$	8.0.157351936.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{3}+\beta _{7}q^{7}-\beta _{3}q^{9}-2q^{11}+\cdots\)
2100.2.x.c	$2100$	$2$	2100.x	35.f	$4$	$16$	$8$	$16.769$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+(\beta _{12}-\beta _{13}-\beta _{14})q^{7}-\beta _{11}q^{9}+\cdots\)
2100.2.x.d	$2100$	$2$	2100.x	35.f	$4$	$16$	$8$	$16.769$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{8}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{10})q^{7}-\beta _{5}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)