Space of modular forms of level 1296, weight 5, and Character 1296.e

• Label: 1296.5.e
• Level: $1296$
• Weight: $5$
• Character orbit: 1296.e
• Rep. character: $\chi_{1296}(161,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $10$
• Sturm bound: $1080$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	1296.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1080\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(1296, [\chi])\).

	Total	New	Old
Modular forms	900	98	802
Cusp forms	828	94	734
Eisenstein series	72	4	68

Trace form

\( 94 q - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(1296, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1296.5.e.a	$1296$	$5$	1296.e	3.b	$2$	$4$	$4$	$133.967$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(52\)	$3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}+\beta _{2})q^{5}+(13-\beta _{3})q^{7}+(-17\beta _{1}+\cdots)q^{11}+\cdots\)
1296.5.e.b	$1296$	$5$	1296.e	3.b	$2$	$4$	$4$	$133.967$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(52\)	$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(9\beta _{1}-4\beta _{2})q^{5}+(13-13\beta _{3})q^{7}+\cdots\)
1296.5.e.c	$1296$	$5$	1296.e	3.b	$2$	$6$	$6$	$133.967$	6.0.39400128.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(24\)	$2^{3}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+(4-\beta _{2}-\beta _{3})q^{7}+(-5\beta _{1}+\cdots)q^{11}+\cdots\)
1296.5.e.d	$1296$	$5$	1296.e	3.b	$2$	$8$	$8$	$133.967$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-52\)	$2^{2}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{5}+(-6+\beta _{3})q^{7}+(-3\beta _{1}+\cdots)q^{11}+\cdots\)
1296.5.e.e	$1296$	$5$	1296.e	3.b	$2$	$8$	$8$	$133.967$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-52\)	$2^{10}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(-6-\beta _{1})q^{7}+(-2\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
1296.5.e.f	$1296$	$5$	1296.e	3.b	$2$	$8$	$8$	$133.967$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-52\)	$2^{2}\cdot 3^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(-7+\beta _{1})q^{7}-\beta _{5}q^{11}+\cdots\)
1296.5.e.g	$1296$	$5$	1296.e	3.b	$2$	$8$	$8$	$133.967$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(26\)	$2^{6}\cdot 3^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(3-\beta _{3})q^{7}+\beta _{2}q^{11}+(2+\cdots)q^{13}+\cdots\)
1296.5.e.h	$1296$	$5$	1296.e	3.b	$2$	$12$	$12$	$133.967$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-96\)	$2^{10}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{4})q^{5}+(-8+\beta _{8})q^{7}+\cdots\)
1296.5.e.i	$1296$	$5$	1296.e	3.b	$2$	$12$	$12$	$133.967$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(96\)	$2^{10}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{8})q^{5}+(8-\beta _{4})q^{7}+(-12\beta _{1}+\cdots)q^{11}+\cdots\)
1296.5.e.j	$1296$	$5$	1296.e	3.b	$2$	$24$	$24$	$133.967$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)