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

• Label: 2160.3.e
• Level: $2160$
• Weight: $3$
• Character orbit: 2160.e
• Rep. character: $\chi_{2160}(271,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $1296$
• Trace bound: $37$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2160.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1296\)
Trace bound:			\(37\)
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	64	836
Cusp forms	828	64	764
Eisenstein series	72	0	72

Trace form

\( 64 q + O(q^{10}) \)

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.e.a	$2160$	$3$	2160.e	4.b	$2$	$4$	$4$	$58.856$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			2160.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+2\beta _{2}q^{11}-8q^{13}+3\beta _{1}q^{17}+\cdots\)
2160.3.e.b	$2160$	$3$	2160.e	4.b	$2$	$4$	$4$	$58.856$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			2160.3.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+2\beta _{3}q^{7}+4\beta _{2}q^{11}+22q^{13}+\cdots\)
2160.3.e.c	$2160$	$3$	2160.e	4.b	$2$	$8$	$8$	$58.856$	8.0.121550625.1	None		✓			2160.3.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(\beta _{2}-\beta _{7})q^{7}+(2\beta _{4}-\beta _{5}+\cdots)q^{11}+\cdots\)
2160.3.e.d	$2160$	$3$	2160.e	4.b	$2$	$12$	$12$	$58.856$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2160.3.e.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{2}q^{7}-\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)
2160.3.e.e	$2160$	$3$	2160.e	4.b	$2$	$12$	$12$	$58.856$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2160.3.e.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{2}q^{7}+\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)
2160.3.e.f	$2160$	$3$	2160.e	4.b	$2$	$12$	$12$	$58.856$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2160.3.e.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{9}q^{11}+(1+\beta _{3}+\cdots)q^{13}+\cdots\)
2160.3.e.g	$2160$	$3$	2160.e	4.b	$2$	$12$	$12$	$58.856$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2160.3.e.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(\beta _{3}-\beta _{8})q^{7}+\beta _{10}q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)