Space of modular forms of level 1575, weight 1, and Character 1575.h

• Label: 1575.1.h
• Level: $1575$
• Weight: $1$
• Character orbit: 1575.h
• Rep. character: $\chi_{1575}(1126,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1575.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1575, [\chi])\).

	Total	New	Old
Modular forms	40	10	30
Cusp forms	16	7	9
Eisenstein series	24	3	21

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	7	0	0	0

Trace form

\( 7 q + 7 q^{4} + q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1575, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1575.1.h.a	$1575$	$1$	1575.h	7.b	$2$	$1$	$1$	$0.786$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-7}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q-q^{2}-q^{7}+q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
1575.1.h.b	$1575$	$1$	1575.h	7.b	$2$	$1$	$1$	$0.786$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q-q^{4}+q^{7}+q^{16}-q^{28}+2q^{37}+\cdots\)
1575.1.h.c	$1575$	$1$	1575.h	7.b	$2$	$1$	$1$	$0.786$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-7}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
1575.1.h.d	$1575$	$1$	1575.h	7.b	$2$	$2$	$2$	$0.786$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-7}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}-\beta q^{11}+\cdots\)
1575.1.h.e	$1575$	$1$	1575.h	7.b	$2$	$2$	$2$	$0.786$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-7}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\beta q^{2}+2q^{4}+q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)