Space of modular forms of level 1800, weight 1, and Character 1800.c

• Label: 1800.1.c
• Level: $1800$
• Weight: $1$
• Character orbit: 1800.c
• Rep. character: $\chi_{1800}(449,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $360$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1800.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(360\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).

	Total	New	Old
Modular forms	60	4	56
Cusp forms	12	4	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	0	0	4	0

Trace form

\( 4 q - 4 q^{19} + 4 q^{31} + 4 q^{61} - 4 q^{91}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1800.1.c.a	$1800$	$1$	1800.c	15.d	$2$	$4$	$4$	$0.898$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓	✓	✓	1800.1.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+\zeta_{8}^{2}q^{7}+(-\zeta_{8}-\zeta_{8}^{3})q^{11}+\zeta_{8}^{2}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)