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

• Label: 1575.1.cb
• Level: $1575$
• Weight: $1$
• Character orbit: 1575.cb
• Rep. character: $\chi_{1575}(718,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1575.cb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	56	24	32
Cusp forms	8	8	0
Eisenstein series	48	16	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	8	0	0

Trace form

\( 8 q + 4 q^{6} + O(q^{10}) \)

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.cb.a	$1575$	$1$	1575.cb	315.at	$12$	$8$	$2$	$0.786$	\(\Q(\zeta_{24})\)	$A_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{9}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{6}+\cdots\)