Space of modular forms of level 2800, weight 2, and Character 2800.g

• Label: 2800.2.g
• Level: $2800$
• Weight: $2$
• Character orbit: 2800.g
• Rep. character: $\chi_{2800}(449,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $22$
• Sturm bound: $960$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2800.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(960\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2800, [\chi])\).

	Total	New	Old
Modular forms	516	54	462
Cusp forms	444	54	390
Eisenstein series	72	0	72

Trace form

\( 54 q - 54 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2800.2.g.a	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					350.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-iq^{7}-6q^{9}+5q^{11}-6iq^{13}+\cdots\)
2800.2.g.b	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					280.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+iq^{7}-6q^{9}+5q^{11}-5iq^{13}+\cdots\)
2800.2.g.c	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					140.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+iq^{7}-6q^{9}+5q^{11}+3iq^{13}+\cdots\)
2800.2.g.d	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					1400.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-iq^{7}-q^{9}-5q^{11}+8iq^{17}+\cdots\)
2800.2.g.e	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					700.2.a.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{7}-q^{9}-3q^{11}-4iq^{13}+\cdots\)
2800.2.g.f	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					1400.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
2800.2.g.g	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					56.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-iq^{7}-q^{9}-2iq^{17}-2q^{19}+\cdots\)
2800.2.g.h	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					14.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{7}-q^{9}-4iq^{13}-6iq^{17}+\cdots\)
2800.2.g.i	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					350.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{7}+2q^{9}-3q^{11}-2iq^{13}+\cdots\)
2800.2.g.j	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					140.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{7}+2q^{9}-3q^{11}+iq^{13}+\cdots\)
2800.2.g.k	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					1400.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}+2q^{9}+q^{11}+6iq^{13}+\cdots\)
2800.2.g.l	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					35.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{7}+2q^{9}+3q^{11}-5iq^{13}+\cdots\)
2800.2.g.m	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					280.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{7}+2q^{9}+5q^{11}+iq^{13}+\cdots\)
2800.2.g.n	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					70.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+3q^{9}-4q^{11}+6iq^{13}+2iq^{17}+\cdots\)
2800.2.g.o	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					1400.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+3q^{9}-q^{11}-2iq^{13}+4iq^{17}+\cdots\)
2800.2.g.p	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					56.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+3q^{9}+4q^{11}-2iq^{13}-6iq^{17}+\cdots\)
2800.2.g.q	$2800$	$2$	2800.g	5.b	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-1}) \)	None					700.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{7}+3q^{9}+5q^{11}+6iq^{13}+4iq^{17}+\cdots\)
2800.2.g.r	$2800$	$2$	2800.g	5.b	$2$	$4$	$4$	$22.358$	\(\Q(i, \sqrt{33})\)	None					280.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-6+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots\)
2800.2.g.s	$2800$	$2$	2800.g	5.b	$2$	$4$	$4$	$22.358$	\(\Q(i, \sqrt{5})\)	None					175.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{7}+(-3+2\beta _{3})q^{9}+\cdots\)
2800.2.g.t	$2800$	$2$	2800.g	5.b	$2$	$4$	$4$	$22.358$	\(\Q(i, \sqrt{17})\)	None					35.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
2800.2.g.u	$2800$	$2$	2800.g	5.b	$2$	$4$	$4$	$22.358$	\(\Q(i, \sqrt{17})\)	None					280.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
2800.2.g.v	$2800$	$2$	2800.g	5.b	$2$	$4$	$4$	$22.358$	\(\Q(i, \sqrt{17})\)	None					1400.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 2}\)