Space of modular forms of level 6480, weight 2, and Character 6480.h

• Label: 6480.2.h
• Level: $6480$
• Weight: $2$
• Character orbit: 6480.h
• Rep. character: $\chi_{6480}(2591,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $2592$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6480.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2592\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6480, [\chi])\).

	Total	New	Old
Modular forms	1368	96	1272
Cusp forms	1224	96	1128
Eisenstein series	144	0	144

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(6480, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6480.2.h.a	$6480$	$2$	6480.h	12.b	$2$	$16$	$16$	$51.743$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{10}q^{7}+(-1-\beta _{6}+\beta _{15})q^{11}+\cdots\)
6480.2.h.b	$6480$	$2$	6480.h	12.b	$2$	$16$	$16$	$51.743$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{11}q^{5}+(\beta _{8}-\beta _{12}-\beta _{14})q^{7}-\beta _{2}q^{11}+\cdots\)
6480.2.h.c	$6480$	$2$	6480.h	12.b	$2$	$16$	$16$	$51.743$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+\beta _{12}q^{7}-\beta _{7}q^{11}+(-1+\cdots)q^{13}+\cdots\)
6480.2.h.d	$6480$	$2$	6480.h	12.b	$2$	$16$	$16$	$51.743$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{5}+(\beta _{8}-\beta _{12}-\beta _{14})q^{7}+\beta _{2}q^{11}+\cdots\)
6480.2.h.e	$6480$	$2$	6480.h	12.b	$2$	$16$	$16$	$51.743$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}-\beta _{7}q^{7}+\beta _{8}q^{11}+(1+\beta _{10}+\cdots)q^{13}+\cdots\)
6480.2.h.f	$6480$	$2$	6480.h	12.b	$2$	$16$	$16$	$51.743$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-\beta _{10}q^{7}+(1+\beta _{6}-\beta _{15})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(6480, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6480, [\chi]) \cong \)