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}$