Space of modular forms of level 2400, weight 2, and Character 2400.k

• Label: 2400.2.k
• Level: $2400$
• Weight: $2$
• Character orbit: 2400.k
• Rep. character: $\chi_{2400}(1201,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $6$
• Sturm bound: $960$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(960\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2400, [\chi])\).

	Total	New	Old
Modular forms	528	38	490
Cusp forms	432	38	394
Eisenstein series	96	0	96

Trace form

\( 38 q + 4 q^{7} - 38 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2400.2.k.a	$2400$	$2$	2400.k	8.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-2q^{7}-q^{9}-4iq^{13}+2q^{17}+\cdots\)
2400.2.k.b	$2400$	$2$	2400.k	8.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2q^{7}-q^{9}+4iq^{11}+6q^{17}+\cdots\)
2400.2.k.c	$2400$	$2$	2400.k	8.b	$2$	$6$	$6$	$19.164$	6.0.399424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(1-\beta _{3})q^{7}-q^{9}+(\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
2400.2.k.d	$2400$	$2$	2400.k	8.b	$2$	$8$	$8$	$19.164$	8.0.214798336.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-1-\beta _{1})q^{7}-q^{9}-\beta _{5}q^{11}+\cdots\)
2400.2.k.e	$2400$	$2$	2400.k	8.b	$2$	$8$	$8$	$19.164$	8.0.214798336.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(1+\beta _{1})q^{7}-q^{9}+\beta _{5}q^{11}+\cdots\)
2400.2.k.f	$2400$	$2$	2400.k	8.b	$2$	$12$	$12$	$19.164$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{5}q^{7}-q^{9}+\beta _{7}q^{11}+(\beta _{3}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)