Space of modular forms of level 2256, weight 2, and trivial character

• Label: 2256.2.a
• Level: $2256$
• Weight: $2$
• Character orbit: 2256.a
• Rep. character: $\chi_{2256}(1,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $26$
• Sturm bound: $768$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2256 = 2^{4} \cdot 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2256.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(768\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2256))\).

	Total	New	Old
Modular forms	396	46	350
Cusp forms	373	46	327
Eisenstein series	23	0	23

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

\(2\)	\(3\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(+\)	\(-\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(-\)	$-$	\(7\)
Plus space			\(+\)	\(19\)
Minus space			\(-\)	\(27\)

Trace form

\( 46 q - 2 q^{3} + 4 q^{5} + 46 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2256))\) 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	47
2256.2.a.a	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}-5q^{11}-4q^{13}+\cdots\)
2256.2.a.b	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
2256.2.a.c	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+3q^{7}+q^{9}+5q^{11}+\cdots\)
2256.2.a.d	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2256.2.a.e	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
2256.2.a.f	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2256.2.a.g	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2256.2.a.h	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
2256.2.a.i	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
2256.2.a.j	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
2256.2.a.k	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
2256.2.a.l	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+6q^{13}-6q^{17}+\cdots\)
2256.2.a.m	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
2256.2.a.n	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
2256.2.a.o	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+6q^{11}+2q^{15}+\cdots\)
2256.2.a.p	$2256$	$2$	2256.a	1.a	$1$	$1$	$1$	$18.014$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+5q^{7}+q^{9}-3q^{11}+\cdots\)
2256.2.a.q	$2256$	$2$	2256.a	1.a	$1$	$2$	$2$	$18.014$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-2q^{7}+q^{9}+\beta q^{11}+\cdots\)
2256.2.a.r	$2256$	$2$	2256.a	1.a	$1$	$2$	$2$	$18.014$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots\)
2256.2.a.s	$2256$	$2$	2256.a	1.a	$1$	$2$	$2$	$18.014$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
2256.2.a.t	$2256$	$2$	2256.a	1.a	$1$	$3$	$3$	$18.014$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
2256.2.a.u	$2256$	$2$	2256.a	1.a	$1$	$3$	$3$	$18.014$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
2256.2.a.v	$2256$	$2$	2256.a	1.a	$1$	$3$	$3$	$18.014$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2256.2.a.w	$2256$	$2$	2256.a	1.a	$1$	$3$	$3$	$18.014$	3.3.2700.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
2256.2.a.x	$2256$	$2$	2256.a	1.a	$1$	$3$	$3$	$18.014$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
2256.2.a.y	$2256$	$2$	2256.a	1.a	$1$	$4$	$4$	$18.014$	4.4.11348.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(1\)	\(-7\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+q^{9}+\cdots\)
2256.2.a.z	$2256$	$2$	2256.a	1.a	$1$	$5$	$5$	$18.014$	5.5.2324776.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{3})q^{5}+\beta _{4}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2256))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2256)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(141))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(282))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(564))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1128))\)\(^{\oplus 2}\)