Space of modular forms of level 2400, weight 1, and Character 2400.n

• Label: 2400.1.n
• Level: $2400$
• Weight: $1$
• Character orbit: 2400.n
• Rep. character: $\chi_{2400}(401,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2400.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2400, [\chi])\).

	Total	New	Old
Modular forms	56	8	48
Cusp forms	8	2	6
Eisenstein series	48	6	42

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{9} + 4 q^{31} - 2 q^{49} + 4 q^{79} + 2 q^{81}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2400, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2400.1.n.a	$2400$	$1$	2400.n	24.h	$2$	$1$	$1$	$1.198$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)	✓				120.1.i.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{3}+q^{9}-q^{27}+2q^{31}-q^{49}+\cdots\)
2400.1.n.b	$2400$	$1$	2400.n	24.h	$2$	$1$	$1$	$1.198$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)	✓				120.1.i.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}+q^{9}+q^{27}+2q^{31}-q^{49}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2400, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)