Space of modular forms of level 2160, weight 4, and Character 2160.h

• Label: 2160.4.h
• Level: $2160$
• Weight: $4$
• Character orbit: 2160.h
• Rep. character: $\chi_{2160}(431,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $1728$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2160.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1728\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).

	Total	New	Old
Modular forms	1332	96	1236
Cusp forms	1260	96	1164
Eisenstein series	72	0	72

Trace form

\( 96 q - 72 q^{13} - 2400 q^{25} - 504 q^{37} - 4344 q^{49} - 1080 q^{61} + 216 q^{73} + 792 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2160, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2160.4.h.a	$2160$	$4$	2160.h	12.b	$2$	$4$	$4$	$127.444$	\(\Q(\zeta_{12})\)	None		✓			2160.4.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta_1 q^{5}+4\beta_{2} q^{7}+7\beta_{3} q^{11}+\cdots\)
2160.4.h.b	$2160$	$4$	2160.h	12.b	$2$	$4$	$4$	$127.444$	\(\Q(\zeta_{12})\)	None		✓			2160.4.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-5\beta_1 q^{5}-18\beta_{2} q^{7}-28\beta_{3} q^{11}+\cdots\)
2160.4.h.c	$2160$	$4$	2160.h	12.b	$2$	$12$	$12$	$127.444$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2160.4.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta _{1}q^{5}+(-3\beta _{3}+\beta _{8})q^{7}+(-8\beta _{2}+\cdots)q^{11}+\cdots\)
2160.4.h.d	$2160$	$4$	2160.h	12.b	$2$	$12$	$12$	$127.444$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2160.4.h.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{6}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(4\beta _{3}+\beta _{7})q^{7}+(-\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots\)
2160.4.h.e	$2160$	$4$	2160.h	12.b	$2$	$12$	$12$	$127.444$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2160.4.h.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{12}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(\beta _{2}+\beta _{4})q^{7}+\beta _{7}q^{11}+(3^{3}+\cdots)q^{13}+\cdots\)
2160.4.h.f	$2160$	$4$	2160.h	12.b	$2$	$16$	$16$	$127.444$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2160.4.h.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{20}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}-\beta _{1}q^{7}+\beta _{11}q^{11}+(-5+\cdots)q^{13}+\cdots\)
2160.4.h.g	$2160$	$4$	2160.h	12.b	$2$	$16$	$16$	$127.444$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2160.4.h.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-5\beta _{4}q^{5}+(-\beta _{2}+\beta _{8})q^{7}+(-3\beta _{3}+\cdots)q^{11}+\cdots\)
2160.4.h.h	$2160$	$4$	2160.h	12.b	$2$	$20$	$20$	$127.444$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		2160.4.h.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{34}\cdot 3^{18}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{5}+(\beta _{1}-\beta _{4})q^{7}-\beta _{3}q^{11}+(-9+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)