Space of modular forms of level 2736, weight 3, and Character 2736.h

• Label: 2736.3.h
• Level: $2736$
• Weight: $3$
• Character orbit: 2736.h
• Rep. character: $\chi_{2736}(305,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $1440$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2736.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1440\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

	Total	New	Old
Modular forms	984	72	912
Cusp forms	936	72	864
Eisenstein series	48	0	48

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2736.3.h.a	$2736$	$3$	2736.h	3.b	$2$	$4$	$4$	$74.551$	\(\Q(\sqrt{-2}, \sqrt{19})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+3\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+(-3\beta _{1}+\cdots)q^{11}+\cdots\)
2736.3.h.b	$2736$	$3$	2736.h	3.b	$2$	$8$	$8$	$74.551$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2\cdot 3^{3}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{3})q^{7}+(\beta _{5}+\cdots)q^{11}+\cdots\)
2736.3.h.c	$2736$	$3$	2736.h	3.b	$2$	$12$	$12$	$74.551$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{5}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-1-\beta _{4})q^{7}+\beta _{10}q^{11}+\cdots\)
2736.3.h.d	$2736$	$3$	2736.h	3.b	$2$	$12$	$12$	$74.551$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{5}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(1-\beta _{7})q^{7}+(\beta _{2}-\beta _{5}+\beta _{8}+\cdots)q^{11}+\cdots\)
2736.3.h.e	$2736$	$3$	2736.h	3.b	$2$	$16$	$16$	$74.551$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{10})q^{5}+\beta _{3}q^{7}+(\beta _{9}+\beta _{10}+\cdots)q^{11}+\cdots\)
2736.3.h.f	$2736$	$3$	2736.h	3.b	$2$	$20$	$20$	$74.551$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-\beta _{8}+\beta _{16})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)