Space of modular forms of level 2175, weight 1, and Character 2175.b

• Label: 2175.1.b
• Level: $2175$
• Weight: $1$
• Character orbit: 2175.b
• Rep. character: $\chi_{2175}(2174,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $300$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2175.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 435 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(300\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2175, [\chi])\).

	Total	New	Old
Modular forms	36	20	16
Cusp forms	24	16	8
Eisenstein series	12	4	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - 12 q^{4} - 4 q^{6} - 16 q^{9} + 8 q^{16} + 8 q^{24} + 8 q^{34} + 12 q^{36} - 12 q^{49} - 4 q^{51} + 4 q^{54} - 4 q^{64} + 16 q^{81} - 8 q^{91} + 8 q^{94} - 12 q^{96}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2175, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2175.1.b.a	$2175$	$1$	2175.b	435.b	$2$	$2$	$2$	$1.085$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-87}) \)	None					87.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{2}-i q^{3}-q^{6}-i q^{7}-i q^{8}+\cdots\)
2175.1.b.b	$2175$	$1$	2175.b	435.b	$2$	$2$	$2$	$1.085$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-87}) \)	None					87.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{2}-i q^{3}-q^{6}+i q^{7}-i q^{8}+\cdots\)
2175.1.b.c	$2175$	$1$	2175.b	435.b	$2$	$6$	$6$	$1.085$	6.0.419904.1	$D_{9}$	\(\Q(\sqrt{-87}) \)	None		✓			2175.1.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{5}q^{2}-\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2175.1.b.d	$2175$	$1$	2175.b	435.b	$2$	$6$	$6$	$1.085$	6.0.419904.1	$D_{9}$	\(\Q(\sqrt{-87}) \)	None		✓			2175.1.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2175, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2175, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)