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

• Label: 2736.2.k
• Level: $2736$
• Weight: $2$
• Character orbit: 2736.k
• Rep. character: $\chi_{2736}(2431,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $16$
• Sturm bound: $960$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(960\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	504	50	454
Cusp forms	456	50	406
Eisenstein series	48	0	48

Trace form

\( 50 q + O(q^{10}) \)

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.k.a	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{5}+\zeta_{6}q^{7}+3\zeta_{6}q^{11}-4\zeta_{6}q^{13}+\cdots\)
2736.2.k.b	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{5}-\zeta_{6}q^{7}-3\zeta_{6}q^{11}-4\zeta_{6}q^{13}+\cdots\)
2736.2.k.c	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2\zeta_{6}q^{7}-4\zeta_{6}q^{13}+(-4-\zeta_{6})q^{19}+\cdots\)
2736.2.k.d	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2\zeta_{6}q^{7}-4\zeta_{6}q^{13}+(4+\zeta_{6})q^{19}+\cdots\)
2736.2.k.e	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{6}q^{7}+2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+6q^{17}+\cdots\)
2736.2.k.f	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{6}q^{7}+2\zeta_{6}q^{11}+2\zeta_{6}q^{13}+6q^{17}+\cdots\)
2736.2.k.g	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{5}+\beta q^{7}-\beta q^{11}-7q^{17}-\beta q^{19}+\cdots\)
2736.2.k.h	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-2\beta q^{7}-\beta q^{11}+2\beta q^{13}+\cdots\)
2736.2.k.i	$2736$	$2$	2736.k	76.d	$2$	$2$	$2$	$21.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-2\beta q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
2736.2.k.j	$2736$	$2$	2736.k	76.d	$2$	$4$	$4$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.k.k	$2736$	$2$	2736.k	76.d	$2$	$4$	$4$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{7}-2\beta _{2}q^{11}-\beta _{3}q^{13}-3q^{17}+\cdots\)
2736.2.k.l	$2736$	$2$	2736.k	76.d	$2$	$4$	$4$	$21.847$	\(\Q(\sqrt{-6}, \sqrt{19})\)	\(\Q(\sqrt{-57}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{11}+\beta _{2}q^{19}+3\beta _{1}q^{23}-5q^{25}+\cdots\)
2736.2.k.m	$2736$	$2$	2736.k	76.d	$2$	$4$	$4$	$21.847$	\(\Q(i, \sqrt{19})\)	\(\Q(\sqrt{-19}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{5}-\beta _{3}q^{7}+5\beta _{1}q^{11}+\beta _{2}q^{17}+\cdots\)
2736.2.k.n	$2736$	$2$	2736.k	76.d	$2$	$4$	$4$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+(2\beta _{1}-2\beta _{2}+\cdots)q^{13}+\cdots\)
2736.2.k.o	$2736$	$2$	2736.k	76.d	$2$	$4$	$4$	$21.847$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{1}q^{7}+\beta _{1}q^{11}+(2\beta _{1}-2\beta _{2}+\cdots)q^{13}+\cdots\)
2736.2.k.p	$2736$	$2$	2736.k	76.d	$2$	$8$	$8$	$21.847$	8.0.2702336256.1	\(\Q(\sqrt{-19}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{5}+(\beta _{2}-\beta _{3})q^{7}+(-\beta _{6}+\beta _{7})q^{11}+\cdots\)

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

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