Space of modular forms of level 2523, weight 1, and Character 2523.d

• Label: 2523.1.d
• Level: $2523$
• Weight: $1$
• Character orbit: 2523.d
• Rep. character: $\chi_{2523}(2522,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $290$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2523.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(290\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2523, [\chi])\).

	Total	New	Old
Modular forms	38	30	8
Cusp forms	8	4	4
Eisenstein series	30	26	4

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 4 q^{4} - 2 q^{7} - 4 q^{9} + 2 q^{13} + 4 q^{16} + 4 q^{25} + 2 q^{28} + 4 q^{36} + 2 q^{49} - 2 q^{52} + 2 q^{57} + 2 q^{63} - 4 q^{64} + 2 q^{67} + 4 q^{81} + 4 q^{91} + 2 q^{93}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2523, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2523.1.d.a	$2523$	$1$	2523.d	87.d	$2$	$4$	$4$	$1.259$	\(\Q(i, \sqrt{5})\)	$D_{5}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	2523.1.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{7}-q^{9}-\beta _{3}q^{12}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2523, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2523, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)