Space of modular forms of level 2736, weight 2, and Character 2736.s

• Label: 2736.2.s
• Level: $2736$
• Weight: $2$
• Character orbit: 2736.s
• Rep. character: $\chi_{2736}(577,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $98$
• Newform subspaces: $29$
• Sturm bound: $960$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.s (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(960\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

	Total	New	Old
Modular forms	1008	102	906
Cusp forms	912	98	814
Eisenstein series	96	4	92

Trace form

\( 98 q + q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2736.2.s.a	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{5}+3q^{11}-2\zeta_{6}q^{13}+\cdots\)
2736.2.s.b	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{5}+3q^{7}-4q^{11}-5\zeta_{6}q^{13}+\cdots\)
2736.2.s.c	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{5}+3q^{7}+2q^{11}+7\zeta_{6}q^{13}+\cdots\)
2736.2.s.d	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{5}-3q^{7}-2q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.e	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{5}-3q^{7}+6q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.f	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{5}+5q^{7}-4q^{11}-5\zeta_{6}q^{13}+\cdots\)
2736.2.s.g	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{5}-4q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.h	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-5q^{7}-5\zeta_{6}q^{13}+(-3-2\zeta_{6})q^{19}+\cdots\)
2736.2.s.i	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3q^{7}+2q^{11}-\zeta_{6}q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
2736.2.s.j	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{7}-2q^{11}-5\zeta_{6}q^{13}+(-4+4\zeta_{6})q^{17}+\cdots\)
2736.2.s.k	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{7}-2q^{11}+3\zeta_{6}q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
2736.2.s.l	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+q^{7}+7\zeta_{6}q^{13}+(-5+2\zeta_{6})q^{19}+\cdots\)
2736.2.s.m	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4q^{7}+3q^{11}-2\zeta_{6}q^{13}+(-6+6\zeta_{6})q^{17}+\cdots\)
2736.2.s.n	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{5}-3q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.o	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{5}-3q^{7}+2q^{11}+\zeta_{6}q^{13}+\cdots\)
2736.2.s.p	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{5}+3q^{7}-5\zeta_{6}q^{13}+(-4+\cdots)q^{17}+\cdots\)
2736.2.s.q	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{5}-4q^{11}+5\zeta_{6}q^{13}+\cdots\)
2736.2.s.r	$2736$	$2$	2736.s	19.c	$3$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{5}+3q^{7}+4q^{11}-5\zeta_{6}q^{13}+\cdots\)
2736.2.s.s	$2736$	$2$	2736.s	19.c	$3$	$4$	$2$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{3})q^{7}+\cdots\)
2736.2.s.t	$2736$	$2$	2736.s	19.c	$3$	$4$	$2$	$21.847$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{5}+(1-\beta _{3})q^{7}+\beta _{3}q^{11}+(1+\cdots)q^{13}+\cdots\)
2736.2.s.u	$2736$	$2$	2736.s	19.c	$3$	$4$	$2$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
2736.2.s.v	$2736$	$2$	2736.s	19.c	$3$	$4$	$2$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
2736.2.s.w	$2736$	$2$	2736.s	19.c	$3$	$4$	$2$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(3-\beta _{3})q^{11}+\cdots\)
2736.2.s.x	$2736$	$2$	2736.s	19.c	$3$	$6$	$3$	$21.847$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+(-1+\zeta_{18}^{5})q^{7}+\cdots\)
2736.2.s.y	$2736$	$2$	2736.s	19.c	$3$	$6$	$3$	$21.847$	6.0.2696112.1	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}+(1+\beta _{2}-\beta _{3})q^{7}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
2736.2.s.z	$2736$	$2$	2736.s	19.c	$3$	$6$	$3$	$21.847$	6.0.954288.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.s.ba	$2736$	$2$	2736.s	19.c	$3$	$8$	$4$	$21.847$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}+\beta _{5})q^{5}+(1-\beta _{6})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.s.bb	$2736$	$2$	2736.s	19.c	$3$	$8$	$4$	$21.847$	8.0.764411904.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{5}+(1+\beta _{5})q^{7}+(\beta _{1}-\beta _{2}+\beta _{6}+\cdots)q^{11}+\cdots\)
2736.2.s.bc	$2736$	$2$	2736.s	19.c	$3$	$8$	$4$	$21.847$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(1-\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)