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

• Label: 2100.2.d
• Level: $2100$
• Weight: $2$
• Character orbit: 2100.d
• Rep. character: $\chi_{2100}(1301,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $12$
• Sturm bound: $960$
• Trace bound: $43$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(960\)
Trace bound:			\(43\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(37\), \(41\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	516	50	466
Cusp forms	444	50	394
Eisenstein series	72	0	72

Trace form

\( 50 q + 6 q^{9} + 8 q^{21} + 12 q^{37} + 16 q^{43} - 4 q^{49} - 20 q^{51} - 20 q^{63} + 16 q^{79} - 10 q^{81} - 22 q^{91} + 56 q^{93} - 28 q^{99}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2100.2.d.a	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	\(\Q(\sqrt{-3}) \)	None					420.2.d.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
2100.2.d.b	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					84.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}+(-\beta-2)q^{7}-3 q^{9}+4\beta q^{13}+\cdots\)
2100.2.d.c	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			2100.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+2\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}-3q^{9}+\cdots\)
2100.2.d.d	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			2100.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(1-2\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}-3q^{9}+\cdots\)
2100.2.d.e	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	\(\Q(\sqrt{-3}) \)	None					420.2.d.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{6})q^{3}+(-1-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
2100.2.d.f	$2100$	$2$	2100.d	21.c	$2$	$4$	$4$	$16.769$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None					420.2.f.b	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2100.2.d.g	$2100$	$2$	2100.d	21.c	$2$	$4$	$4$	$16.769$	\(\Q(i, \sqrt{5})\)	None					420.2.d.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{3}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\)
2100.2.d.h	$2100$	$2$	2100.d	21.c	$2$	$4$	$4$	$16.769$	\(\Q(i, \sqrt{5})\)	None					420.2.d.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}+(1-\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2100.2.d.i	$2100$	$2$	2100.d	21.c	$2$	$4$	$4$	$16.769$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None					420.2.f.b	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2100.2.d.j	$2100$	$2$	2100.d	21.c	$2$	$8$	$8$	$16.769$	\(\Q(\sqrt{-3}, \sqrt{5}, \sqrt{-7})\)	\(\Q(\sqrt{-35}) \)					420.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{2}+\beta _{3})q^{7}-\beta _{1}q^{9}+\cdots\)
2100.2.d.k	$2100$	$2$	2100.d	21.c	$2$	$8$	$8$	$16.769$	8.0.\(\cdots\).1	None		✓			2100.2.d.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3}-\beta _{6})q^{3}+(\beta _{3}+\beta _{5})q^{7}+\cdots\)
2100.2.d.l	$2100$	$2$	2100.d	21.c	$2$	$8$	$8$	$16.769$	8.0.\(\cdots\).1	None		✓			2100.2.d.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3}-\beta _{6})q^{3}+(\beta _{3}-\beta _{5})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)