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

• Label: 2400.2.f
• Level: $2400$
• Weight: $2$
• Character orbit: 2400.f
• Rep. character: $\chi_{2400}(1249,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $18$
• Sturm bound: $960$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(960\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	528	36	492
Cusp forms	432	36	396
Eisenstein series	96	0	96

Trace form

\( 36 q - 36 q^{9} + O(q^{10}) \)

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.f.a	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}-q^{9}-4q^{11}+2iq^{13}+\cdots\)
2400.2.f.b	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}-4q^{11}+7iq^{13}+\cdots\)
2400.2.f.c	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots\)
2400.2.f.d	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{7}-q^{9}-4q^{11}-6iq^{13}+\cdots\)
2400.2.f.e	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-q^{9}-4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
2400.2.f.f	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}-5iq^{13}-5q^{19}+\cdots\)
2400.2.f.g	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{9}+2iq^{13}-6iq^{17}-4q^{19}+\cdots\)
2400.2.f.h	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{7}-q^{9}-iq^{13}-3q^{19}+\cdots\)
2400.2.f.i	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{7}-q^{9}-2iq^{13}+6iq^{17}+\cdots\)
2400.2.f.j	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{7}-q^{9}+2iq^{13}-6iq^{17}+\cdots\)
2400.2.f.k	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{7}-q^{9}+iq^{13}+3q^{19}+\cdots\)
2400.2.f.l	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{9}-2iq^{13}+6iq^{17}+4q^{19}+\cdots\)
2400.2.f.m	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}+5iq^{13}+5q^{19}+\cdots\)
2400.2.f.n	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
2400.2.f.o	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{7}-q^{9}+4q^{11}+6iq^{13}+\cdots\)
2400.2.f.p	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots\)
2400.2.f.q	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}+4q^{11}-7iq^{13}+\cdots\)
2400.2.f.r	$2400$	$2$	2400.f	5.b	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}-q^{9}+4q^{11}-2iq^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)