Space of modular forms of level 2736, weight 2, and trivial character

• Label: 2736.2.a
• Level: $2736$
• Weight: $2$
• Character orbit: 2736.a
• Rep. character: $\chi_{2736}(1,\cdot)$
• Character field: $\Q$
• Dimension: $45$
• Newform subspaces: $32$
• 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.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 32 \)
Sturm bound:			\(960\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2736))\).

	Total	New	Old
Modular forms	504	45	459
Cusp forms	457	45	412
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(+\)	\(-\)	$-$	\(8\)
\(+\)	\(-\)	\(+\)	$-$	\(8\)
\(+\)	\(-\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(+\)	$-$	\(4\)
\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(7\)
Plus space			\(+\)	\(18\)
Minus space			\(-\)	\(27\)

Trace form

\( 45 q - 2 q^{5} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	19
2736.2.a.a	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-4q^{11}-4q^{13}-6q^{17}+\cdots\)
2736.2.a.b	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-6q^{11}+2q^{13}-4q^{17}+q^{19}+\cdots\)
2736.2.a.c	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.d	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}+2q^{13}+6q^{17}+q^{19}+\cdots\)
2736.2.a.e	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{13}-2q^{17}+q^{19}-q^{25}+\cdots\)
2736.2.a.f	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{11}-4q^{13}+q^{19}+8q^{23}+\cdots\)
2736.2.a.g	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{11}+2q^{13}-6q^{17}+q^{19}+\cdots\)
2736.2.a.h	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}-3q^{11}-6q^{13}-3q^{17}+\cdots\)
2736.2.a.i	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-5q^{11}-2q^{13}+q^{17}+\cdots\)
2736.2.a.j	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}+2q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.k	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+2q^{11}+q^{13}+5q^{17}-q^{19}+\cdots\)
2736.2.a.l	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{11}-2q^{13}+4q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.m	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{11}-2q^{13}-4q^{17}-q^{19}+2q^{23}+\cdots\)
2736.2.a.n	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-6q^{11}+5q^{13}-3q^{17}-q^{19}+\cdots\)
2736.2.a.o	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{13}-6q^{17}-q^{19}-6q^{23}+\cdots\)
2736.2.a.p	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-3q^{11}-4q^{13}-5q^{17}+\cdots\)
2736.2.a.q	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.r	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{11}-4q^{13}+q^{19}-8q^{23}+\cdots\)
2736.2.a.s	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+6q^{13}+6q^{17}+q^{19}+4q^{23}+\cdots\)
2736.2.a.t	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-5q^{11}-6q^{13}+5q^{17}+\cdots\)
2736.2.a.u	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+3q^{7}-q^{11}-2q^{13}+5q^{17}+\cdots\)
2736.2.a.v	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+5q^{7}+q^{11}+2q^{13}+q^{17}+\cdots\)
2736.2.a.w	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-3q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots\)
2736.2.a.x	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+6q^{11}+2q^{13}+4q^{17}+q^{19}+\cdots\)
2736.2.a.y	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-1+\cdots)q^{11}+\cdots\)
2736.2.a.z	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-\beta q^{7}+(4-\beta )q^{11}-2\beta q^{13}+\cdots\)
2736.2.a.ba	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{7}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-3q^{7}-\beta q^{11}+2q^{13}-3\beta q^{17}+\cdots\)
2736.2.a.bb	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots\)
2736.2.a.bc	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.892.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2736.2.a.bd	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.961.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.a.be	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.892.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{11}+\cdots\)
2736.2.a.bf	$2736$	$2$	2736.a	1.a	$1$	$4$	$4$	$21.847$	4.4.13068.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2736))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2736)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 2}\)