Space of modular forms of level 2160, weight 3, and Character 2160.c

• Label: 2160.3.c
• Level: $2160$
• Weight: $3$
• Character orbit: 2160.c
• Rep. character: $\chi_{2160}(1889,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $17$
• Sturm bound: $1296$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2160.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1296\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2160, [\chi])\).

	Total	New	Old
Modular forms	900	96	804
Cusp forms	828	96	732
Eisenstein series	72	0	72

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2160, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2160.3.c.a	$2160$	$3$	2160.c	15.d	$2$	$2$	$2$	$58.856$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-15}) \)	✓				135.3.d.c	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-5q^{5}+(-7-\beta )q^{17}+(-11+\beta )q^{19}+\cdots\)
2160.3.c.b	$2160$	$3$	2160.c	15.d	$2$	$2$	$2$	$58.856$	\(\Q(\sqrt{-1}) \)	None					135.3.d.b	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-4-i)q^{5}+2iq^{7}+7iq^{11}+5iq^{13}+\cdots\)
2160.3.c.c	$2160$	$3$	2160.c	15.d	$2$	$2$	$2$	$58.856$	\(\Q(\sqrt{-11}) \)	None					135.3.d.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}+(1-2\beta )q^{7}+(1-2\beta )q^{11}+\cdots\)
2160.3.c.d	$2160$	$3$	2160.c	15.d	$2$	$2$	$2$	$58.856$	\(\Q(\sqrt{-11}) \)	None					135.3.d.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+(1-2\beta )q^{7}+(-1+2\beta )q^{11}+\cdots\)
2160.3.c.e	$2160$	$3$	2160.c	15.d	$2$	$2$	$2$	$58.856$	\(\Q(\sqrt{-1}) \)	None					135.3.d.b	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(4+i)q^{5}+2iq^{7}-7iq^{11}+5iq^{13}+\cdots\)
2160.3.c.f	$2160$	$3$	2160.c	15.d	$2$	$2$	$2$	$58.856$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-15}) \)	✓				135.3.d.c	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+5q^{5}+(7+\beta )q^{17}+(-11+\beta )q^{19}+\cdots\)
2160.3.c.g	$2160$	$3$	2160.c	15.d	$2$	$4$	$4$	$58.856$	4.0.31744.1	None					270.3.b.a	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\)
2160.3.c.h	$2160$	$3$	2160.c	15.d	$2$	$4$	$4$	$58.856$	\(\Q(\sqrt{-11}, \sqrt{-19})\)	None					540.3.b.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{11}+\cdots\)
2160.3.c.i	$2160$	$3$	2160.c	15.d	$2$	$4$	$4$	$58.856$	\(\Q(\zeta_{8})\)	None					270.3.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\zeta_{8}^{3}q^{5}+5\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
2160.3.c.j	$2160$	$3$	2160.c	15.d	$2$	$4$	$4$	$58.856$	\(\Q(\zeta_{8})\)	None					270.3.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(4\zeta_{8}-3\zeta_{8}^{3})q^{5}-11\zeta_{8}^{2}q^{7}+(5\zeta_{8}+\cdots)q^{11}+\cdots\)
2160.3.c.k	$2160$	$3$	2160.c	15.d	$2$	$4$	$4$	$58.856$	\(\Q(i, \sqrt{10})\)	None					135.3.d.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{3})q^{5}+\beta _{1}q^{7}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
2160.3.c.l	$2160$	$3$	2160.c	15.d	$2$	$4$	$4$	$58.856$	\(\Q(\sqrt{-11}, \sqrt{-19})\)	None					540.3.b.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+(2\beta _{1}+3\beta _{2}+\cdots)q^{11}+\cdots\)
2160.3.c.m	$2160$	$3$	2160.c	15.d	$2$	$4$	$4$	$58.856$	4.0.31744.1	None					270.3.b.a	$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\)
2160.3.c.n	$2160$	$3$	2160.c	15.d	$2$	$8$	$8$	$58.856$	8.0.\(\cdots\).13	None					540.3.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}-\beta _{6}q^{11}+\cdots\)
2160.3.c.o	$2160$	$3$	2160.c	15.d	$2$	$12$	$12$	$58.856$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					1080.3.c.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{5}-\beta _{5}q^{7}+\beta _{9}q^{11}+\beta _{8}q^{13}+\cdots\)
2160.3.c.p	$2160$	$3$	2160.c	15.d	$2$	$12$	$12$	$58.856$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					1080.3.c.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{5}-\beta _{5}q^{7}-\beta _{9}q^{11}+\beta _{8}q^{13}+\cdots\)
2160.3.c.q	$2160$	$3$	2160.c	15.d	$2$	$24$	$24$	$58.856$		None			✓		1080.3.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)