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

• Label: 2475.1.ev
• Level: $2475$
• Weight: $1$
• Character orbit: 2475.ev
• Rep. character: $\chi_{2475}(439,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $16$
• 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.ev (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2475 \)
Character field:			\(\Q(\zeta_{30})\)
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	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - 2 q^{4} - 4 q^{5} + 2 q^{9} + O(q^{10}) \)

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.ev.a	$2475$	$1$	2475.ev	2475.dv	$30$	$8$	$1$	$1.235$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(-8\)	\(0\)	$1$		\(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{4}q^{4}-q^{5}+\zeta_{30}^{14}q^{9}+\cdots\)
2475.1.ev.b	$2475$	$1$	2475.ev	2475.dv	$30$	$8$	$1$	$1.235$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(1\)	\(4\)	\(0\)	$1$		\(q-\zeta_{30}q^{3}-\zeta_{30}^{4}q^{4}+\zeta_{30}^{5}q^{5}+\zeta_{30}^{2}q^{9}+\cdots\)