Space of modular forms of level 3575, weight 1, and Character 3575.h

• Label: 3575.1.h
• Level: $3575$
• Weight: $1$
• Character orbit: 3575.h
• Rep. character: $\chi_{3575}(2001,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $11$
• Sturm bound: $420$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3575 = 5^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3575.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 143 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(420\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3575, [\chi])\).

	Total	New	Old
Modular forms	52	34	18
Cusp forms	40	28	12
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	28	0	0	0

Trace form

\( 28 q + 2 q^{3} + 26 q^{4} + 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3575, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3575.1.h.a	$3575$	$1$	3575.h	143.d	$2$	$1$	$1$	$1.784$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(-1\)	\(-2\)	\(0\)	\(-1\)	$1$		\(q-q^{2}-2q^{3}+2q^{6}-q^{7}+q^{8}+3q^{9}+\cdots\)
3575.1.h.b	$3575$	$1$	3575.h	143.d	$2$	$1$	$1$	$1.784$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(0\)	\(-1\)	$1$		\(q-q^{2}+2q^{3}-2q^{6}-q^{7}+q^{8}+3q^{9}+\cdots\)
3575.1.h.c	$3575$	$1$	3575.h	143.d	$2$	$1$	$1$	$1.784$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(0\)	\(1\)	$1$		\(q+q^{2}-2q^{3}-2q^{6}+q^{7}-q^{8}+3q^{9}+\cdots\)
3575.1.h.d	$3575$	$1$	3575.h	143.d	$2$	$1$	$1$	$1.784$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(0\)	\(1\)	$1$		\(q+q^{2}+2q^{3}+2q^{6}+q^{7}-q^{8}+3q^{9}+\cdots\)
3575.1.h.e	$3575$	$1$	3575.h	143.d	$2$	$2$	$2$	$1.784$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
3575.1.h.f	$3575$	$1$	3575.h	143.d	$2$	$2$	$2$	$1.784$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(1\)	$1$		\(q+(1-\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
3575.1.h.g	$3575$	$1$	3575.h	143.d	$2$	$4$	$4$	$1.784$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(-1\)	\(-2\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{3})q^{3}+\cdots\)
3575.1.h.h	$3575$	$1$	3575.h	143.d	$2$	$4$	$4$	$1.784$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta _{1}-\beta _{3})q^{2}+(1+\beta _{3})q^{3}+\cdots\)
3575.1.h.i	$3575$	$1$	3575.h	143.d	$2$	$4$	$4$	$1.784$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-55}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+q^{4}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
3575.1.h.j	$3575$	$1$	3575.h	143.d	$2$	$4$	$4$	$1.784$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(0\)	\(1\)	$1$		\(q+(1-\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{3})q^{3}+\cdots\)
3575.1.h.k	$3575$	$1$	3575.h	143.d	$2$	$4$	$4$	$1.784$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(0\)	\(1\)	$1$		\(q+(1-\beta _{1}+\beta _{3})q^{2}+(1+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3575, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3575, [\chi]) \cong \)