Space of modular forms of level 2100, weight 1, and Character 2100.m

• Label: 2100.1.m
• Level: $2100$
• Weight: $1$
• Character orbit: 2100.m
• Rep. character: $\chi_{2100}(251,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $4$
• Sturm bound: $480$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2100.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(480\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2100, [\chi])\).

	Total	New	Old
Modular forms	28	16	12
Cusp forms	4	4	0
Eisenstein series	24	12	12

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 4 q^{4} + 4 q^{9} + 4 q^{16} - 4 q^{21} + 4 q^{36} - 8 q^{46} + 4 q^{49} + 4 q^{64} + 4 q^{81} - 4 q^{84}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2100.1.m.a	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{105}) \)	✓				420.1.o.a	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
2100.1.m.b	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{105}) \)	✓				420.1.o.a	$4$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2100.1.m.c	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{105}) \)	✓				420.1.o.a	$4$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
2100.1.m.d	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{105}) \)	✓				420.1.o.a	$4$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)