Space of modular forms of level 4080, weight 2, and Character 4080.m

• Label: 4080.2.m
• Level: $4080$
• Weight: $2$
• Character orbit: 4080.m
• Rep. character: $\chi_{4080}(2449,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $21$
• Sturm bound: $1728$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 4080 = 2^{4} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4080.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1728\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(7\), \(11\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4080, [\chi])\).

	Total	New	Old
Modular forms	888	96	792
Cusp forms	840	96	744
Eisenstein series	48	0	48

Trace form

\( 96 q - 96 q^{9} - 8 q^{25} - 24 q^{31} + 24 q^{35} + 16 q^{39} + 16 q^{41} - 96 q^{49} + 12 q^{51} - 28 q^{55} - 16 q^{75} + 88 q^{79} + 96 q^{81} - 16 q^{89} - 64 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4080, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4080.2.m.a	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					255.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i-2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
4080.2.m.b	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					1020.2.g.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i-2)q^{5}-q^{9}+(-2 i-1)q^{15}+\cdots\)
4080.2.m.c	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					2040.2.m.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i-2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
4080.2.m.d	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					510.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(i-2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
4080.2.m.e	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					2040.2.m.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-i-2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
4080.2.m.f	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					2040.2.m.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(2 i-1)q^{5}+3 i q^{7}-q^{9}+\cdots\)
4080.2.m.g	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					2040.2.m.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(2 i-1)q^{5}+i q^{7}-q^{9}+\cdots\)
4080.2.m.h	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					1020.2.g.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i+1)q^{5}+3 i q^{7}+\cdots\)
4080.2.m.i	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					2040.2.m.e	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(2 i+1)q^{5}+5 i q^{7}-q^{9}+\cdots\)
4080.2.m.j	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					1020.2.g.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-2 i+1)q^{5}+i q^{7}-q^{9}+\cdots\)
4080.2.m.k	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					2040.2.m.g	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-i+2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
4080.2.m.l	$4080$	$2$	4080.m	5.b	$2$	$2$	$2$	$32.579$	\(\Q(\sqrt{-1}) \)	None					2040.2.m.f	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(i+2)q^{5}-q^{9}-2 q^{11}+\cdots\)
4080.2.m.m	$4080$	$2$	4080.m	5.b	$2$	$4$	$4$	$32.579$	\(\Q(i, \sqrt{5})\)	None					510.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
4080.2.m.n	$4080$	$2$	4080.m	5.b	$2$	$4$	$4$	$32.579$	\(\Q(i, \sqrt{5})\)	None					255.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}-q^{9}+3q^{11}+\cdots\)
4080.2.m.o	$4080$	$2$	4080.m	5.b	$2$	$4$	$4$	$32.579$	\(\Q(i, \sqrt{6})\)	None					510.2.d.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(1+\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
4080.2.m.p	$4080$	$2$	4080.m	5.b	$2$	$6$	$6$	$32.579$	6.0.5161984.1	None					510.2.d.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{5}q^{5}+(\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
4080.2.m.q	$4080$	$2$	4080.m	5.b	$2$	$10$	$10$	$32.579$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					2040.2.m.h	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{8}q^{5}+(\beta _{4}+\beta _{5})q^{7}-q^{9}+\cdots\)
4080.2.m.r	$4080$	$2$	4080.m	5.b	$2$	$10$	$10$	$32.579$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					1020.2.g.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{7}q^{5}+\beta _{9}q^{7}-q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
4080.2.m.s	$4080$	$2$	4080.m	5.b	$2$	$10$	$10$	$32.579$	10.0.\(\cdots\).1	None					255.2.b.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{3}q^{5}+(-\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{7}+\cdots\)
4080.2.m.t	$4080$	$2$	4080.m	5.b	$2$	$12$	$12$	$32.579$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					2040.2.m.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{8}q^{5}-\beta _{7}q^{7}-q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
4080.2.m.u	$4080$	$2$	4080.m	5.b	$2$	$12$	$12$	$32.579$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					2040.2.m.j	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4080, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4080, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(680, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1020, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2040, [\chi])\)\(^{\oplus 2}\)