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

• Label: 1575.1.n
• Level: $1575$
• Weight: $1$
• Character orbit: 1575.n
• Rep. character: $\chi_{1575}(818,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1575.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	80	24	56
Cusp forms	32	24	8
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

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.n.a	$1575$	$1$	1575.n	105.k	$4$	$4$	$2$	$0.786$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-1-\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\cdots\)
1575.1.n.b	$1575$	$1$	1575.n	105.k	$4$	$4$	$2$	$0.786$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(1+\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\cdots\)
1575.1.n.c	$1575$	$1$	1575.n	105.k	$4$	$8$	$4$	$0.786$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(\zeta_{24}^{8}+\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
1575.1.n.d	$1575$	$1$	1575.n	105.k	$4$	$8$	$4$	$0.786$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(-\zeta_{24}^{8}-\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1575, [\chi]) \cong \)