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

• Label: 2736.2.bm
• Level: $2736$
• Weight: $2$
• Character orbit: 2736.bm
• Rep. character: $\chi_{2736}(559,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $100$
• Newform subspaces: $20$
• Sturm bound: $960$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(960\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(23\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	1008	100	908
Cusp forms	912	100	812
Eisenstein series	96	0	96

Trace form

\( 100 q + O(q^{10}) \)

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.bm.a	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{7}+(-2+4\zeta_{6})q^{11}+(-6+\cdots)q^{13}+\cdots\)
2736.2.bm.b	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{7}+(2-4\zeta_{6})q^{11}+(-6+\cdots)q^{13}+\cdots\)
2736.2.bm.c	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-3+6\zeta_{6})q^{7}+(-2+\zeta_{6})q^{13}+\cdots\)
2736.2.bm.d	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3-6\zeta_{6})q^{7}+(-2+\zeta_{6})q^{13}+(5+\cdots)q^{19}+\cdots\)
2736.2.bm.e	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1+2\zeta_{6})q^{7}+(6-3\zeta_{6})q^{13}+(-3+\cdots)q^{19}+\cdots\)
2736.2.bm.f	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1-2\zeta_{6})q^{7}+(6-3\zeta_{6})q^{13}+(3+2\zeta_{6})q^{19}+\cdots\)
2736.2.bm.g	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3-3\zeta_{6})q^{5}+(2-4\zeta_{6})q^{7}+(2-4\zeta_{6})q^{11}+\cdots\)
2736.2.bm.h	$2736$	$2$	2736.bm	76.f	$6$	$2$	$1$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3-3\zeta_{6})q^{5}+(-2+4\zeta_{6})q^{7}+(-2+\cdots)q^{11}+\cdots\)
2736.2.bm.i	$2736$	$2$	2736.bm	76.f	$6$	$4$	$2$	$21.847$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\beta _{2})q^{5}+(1-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
2736.2.bm.j	$2736$	$2$	2736.bm	76.f	$6$	$4$	$2$	$21.847$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\beta _{2})q^{5}+(-1+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
2736.2.bm.k	$2736$	$2$	2736.bm	76.f	$6$	$4$	$2$	$21.847$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{2})q^{5}-2\zeta_{12}^{3}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\)
2736.2.bm.l	$2736$	$2$	2736.bm	76.f	$6$	$6$	$3$	$21.847$	6.0.31726512.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1}-\beta _{3})q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\cdots\)
2736.2.bm.m	$2736$	$2$	2736.bm	76.f	$6$	$6$	$3$	$21.847$	6.0.31726512.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1}-\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
2736.2.bm.n	$2736$	$2$	2736.bm	76.f	$6$	$6$	$3$	$21.847$	6.0.954288.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2}+\beta _{3}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2736.2.bm.o	$2736$	$2$	2736.bm	76.f	$6$	$6$	$3$	$21.847$	6.0.954288.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2}+\beta _{3}+\beta _{4})q^{5}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{7}+\cdots\)
2736.2.bm.p	$2736$	$2$	2736.bm	76.f	$6$	$8$	$4$	$21.847$	8.0.897122304.10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
2736.2.bm.q	$2736$	$2$	2736.bm	76.f	$6$	$8$	$4$	$21.847$	8.0.897122304.10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
2736.2.bm.r	$2736$	$2$	2736.bm	76.f	$6$	$8$	$4$	$21.847$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{6}-\beta _{7})q^{5}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
2736.2.bm.s	$2736$	$2$	2736.bm	76.f	$6$	$8$	$4$	$21.847$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{6}-\beta _{7})q^{5}+(1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
2736.2.bm.t	$2736$	$2$	2736.bm	76.f	$6$	$16$	$8$	$21.847$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{8}q^{5}+(\beta _{3}+\beta _{5})q^{7}+(\beta _{11}-\beta _{12}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)