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

• Label: 2736.2.f
• Level: $2736$
• Weight: $2$
• Character orbit: 2736.f
• Rep. character: $\chi_{2736}(1025,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $9$
• Sturm bound: $960$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(960\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	504	40	464
Cusp forms	456	40	416
Eisenstein series	48	0	48

Trace form

\( 40 q - 8 q^{7} + O(q^{10}) \)

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.f.a	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.b	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.c	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots\)
2736.2.f.d	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2q^{7}+3\beta q^{11}+2\beta q^{13}+\cdots\)
2736.2.f.e	$2736$	$2$	2736.f	57.d	$2$	$4$	$4$	$21.847$	\(\Q(\sqrt{-2}, \sqrt{19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
2736.2.f.f	$2736$	$2$	2736.f	57.d	$2$	$4$	$4$	$21.847$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+2q^{7}-\beta _{1}q^{11}+2\beta _{2}q^{13}+\cdots\)
2736.2.f.g	$2736$	$2$	2736.f	57.d	$2$	$8$	$8$	$21.847$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}-\beta _{4}q^{7}+(-\beta _{3}-\beta _{5})q^{11}+\cdots\)
2736.2.f.h	$2736$	$2$	2736.f	57.d	$2$	$8$	$8$	$21.847$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}-\beta _{4}q^{7}+(-\beta _{3}-\beta _{5})q^{11}+\cdots\)
2736.2.f.i	$2736$	$2$	2736.f	57.d	$2$	$8$	$8$	$21.847$	8.0.\(\cdots\).4	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{6}q^{11}+(\beta _{3}-\beta _{5}+\cdots)q^{17}+\cdots\)

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

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