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

• Label: 2400.1.u
• Level: $2400$
• Weight: $1$
• Character orbit: 2400.u
• Rep. character: $\chi_{2400}(143,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2400.u (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	144	20	124
Cusp forms	48	12	36
Eisenstein series	96	8	88

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2400.1.u.a	$2400$	$1$	2400.u	120.q	$4$	$4$	$2$	$1.198$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{30}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+\zeta_{8}^{3}q^{17}+\zeta_{8}^{2}q^{19}+\cdots\)
2400.1.u.b	$2400$	$1$	2400.u	120.q	$4$	$8$	$4$	$1.198$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{11}q^{3}-\zeta_{24}^{10}q^{9}+(\zeta_{24}^{4}+\zeta_{24}^{8}+\cdots)q^{11}+\cdots\)

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

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