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

• Label: 2175.1.h
• Level: $2175$
• Weight: $1$
• Character orbit: 2175.h
• Rep. character: $\chi_{2175}(1826,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $7$
• Sturm bound: $300$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2175.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
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	24	12
Cusp forms	24	18	6
Eisenstein series	12	6	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	18	0	0	0

Trace form

\( 18 q + 16 q^{4} + 2 q^{6} + 2 q^{7} + 14 q^{9} + O(q^{10}) \)

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.h.a	$2175$	$1$	2175.h	87.d	$2$	$1$	$1$	$1.085$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-87}) \)	None	✓				87.1.d.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)	$1$		\(q-q^{2}+q^{3}-q^{6}+q^{7}+q^{8}+q^{9}+\cdots\)
2175.1.h.b	$2175$	$1$	2175.h	87.d	$2$	$1$	$1$	$1.085$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-87}) \)	None	✓				87.1.d.a	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+q^{2}-q^{3}-q^{6}+q^{7}-q^{8}+q^{9}+\cdots\)
2175.1.h.c	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-87}) \)	None	✓	✓			2175.1.h.c	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$		\(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots\)
2175.1.h.d	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-87}) \)	None	✓	✓			2175.1.h.c	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$		\(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots\)
2175.1.h.e	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-87}) \)	None	✓	✓			2175.1.h.c	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(1-\beta _{1})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
2175.1.h.f	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-87}) \)	None	✓	✓			2175.1.h.c	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(1-\beta _{1})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
2175.1.h.g	$2175$	$1$	2175.h	87.d	$2$	$4$	$4$	$1.085$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{145}) \)			✓		435.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2175, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)