Space of modular forms of level 2475, weight 1, and Character 2475.cr

• Label: 2475.1.cr
• Level: $2475$
• Weight: $1$
• Character orbit: 2475.cr
• Rep. character: $\chi_{2475}(32,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $360$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2475.cr (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 495 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(360\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2475, [\chi])\).

	Total	New	Old
Modular forms	72	24	48
Cusp forms	24	8	16
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	8	0	0	0

Trace form

\( 8 q - 2 q^{3} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2475, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2475.1.cr.a	$2475$	$1$	2475.cr	495.ad	$12$	$4$	$1$	$1.235$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{11}+\cdots\)
2475.1.cr.b	$2475$	$1$	2475.cr	495.ad	$12$	$4$	$1$	$1.235$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{3}-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)