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

• Label: 2100.2.bc
• Level: $2100$
• Weight: $2$
• Character orbit: 2100.bc
• Rep. character: $\chi_{2100}(949,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $960$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(960\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\)

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

\( 48 q + 24 q^{9} + O(q^{10}) \)

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.bc.a	$2100$	$2$	2100.bc	35.j	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-3\zeta_{12}+\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.b	$2100$	$2$	2100.bc	35.j	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.c	$2100$	$2$	2100.bc	35.j	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{3}+(-\zeta_{12}+3\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.d	$2100$	$2$	2100.bc	35.j	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bc.e	$2100$	$2$	2100.bc	35.j	$6$	$8$	$4$	$16.769$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{7}-\beta _{3}q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots\)
2100.2.bc.f	$2100$	$2$	2100.bc	35.j	$6$	$8$	$4$	$16.769$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}q^{3}+(-\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
2100.2.bc.g	$2100$	$2$	2100.bc	35.j	$6$	$8$	$4$	$16.769$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}q^{3}+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{6})q^{7}+\cdots\)
2100.2.bc.h	$2100$	$2$	2100.bc	35.j	$6$	$8$	$4$	$16.769$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{3}-\beta _{6}q^{7}-\beta _{3}q^{9}+(3+3\beta _{3}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)