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

• Label: 2100.2.bo
• Level: $2100$
• Weight: $2$
• Character orbit: 2100.bo
• Rep. character: $\chi_{2100}(1349,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $9$
• 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.bo (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(960\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	1032	96	936
Cusp forms	888	96	792
Eisenstein series	144	0	144

Trace form

\( 96 q + O(q^{10}) \)

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.bo.a	$2100$	$2$	2100.bo	105.p	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	None		$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bo.b	$2100$	$2$	2100.bo	105.p	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bo.c	$2100$	$2$	2100.bo	105.p	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(-3\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bo.d	$2100$	$2$	2100.bo	105.p	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bo.e	$2100$	$2$	2100.bo	105.p	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bo.f	$2100$	$2$	2100.bo	105.p	$6$	$4$	$2$	$16.769$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bo.g	$2100$	$2$	2100.bo	105.p	$6$	$20$	$10$	$16.769$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}-\beta _{13})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{18}+\cdots)q^{7}+\cdots\)
2100.2.bo.h	$2100$	$2$	2100.bo	105.p	$6$	$20$	$10$	$16.769$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-\beta _{18})q^{7}+(-\beta _{7}+\cdots)q^{9}+\cdots\)
2100.2.bo.i	$2100$	$2$	2100.bo	105.p	$6$	$32$	$16$	$16.769$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)