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

• Label: 2736.2.dc
• Level: $2736$
• Weight: $2$
• Character orbit: 2736.dc
• Rep. character: $\chi_{2736}(449,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $960$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.dc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(960\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	1008	80	928
Cusp forms	912	80	832
Eisenstein series	96	0	96

Trace form

\( 80 q + 8 q^{7} + O(q^{10}) \)

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.dc.a	$2736$	$2$	2736.dc	57.f	$6$	$4$	$2$	$21.847$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{5}+(1-2\beta _{1}+\beta _{3})q^{7}+(-2+\cdots)q^{11}+\cdots\)
2736.2.dc.b	$2736$	$2$	2736.dc	57.f	$6$	$4$	$2$	$21.847$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{5}+(1+2\beta _{1}-\beta _{3})q^{7}+(2-4\beta _{2}+\cdots)q^{11}+\cdots\)
2736.2.dc.c	$2736$	$2$	2736.dc	57.f	$6$	$16$	$8$	$21.847$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{10}q^{5}-\beta _{14}q^{7}-\beta _{7}q^{11}+(-2+\cdots)q^{13}+\cdots\)
2736.2.dc.d	$2736$	$2$	2736.dc	57.f	$6$	$16$	$8$	$21.847$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}-\beta _{10})q^{5}+(-\beta _{7}-\beta _{8})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
2736.2.dc.e	$2736$	$2$	2736.dc	57.f	$6$	$20$	$10$	$21.847$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{14}q^{5}+(-\beta _{7}-\beta _{10})q^{7}+(\beta _{6}+\beta _{18}+\cdots)q^{11}+\cdots\)
2736.2.dc.f	$2736$	$2$	2736.dc	57.f	$6$	$20$	$10$	$21.847$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{14}q^{5}+(-\beta _{7}-\beta _{10})q^{7}+(-\beta _{6}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \)