Space of modular forms of level 4256, weight 2, and trivial character

• Label: 4256.2.a
• Level: $4256$
• Weight: $2$
• Character orbit: 4256.a
• Rep. character: $\chi_{4256}(1,\cdot)$
• Character field: $\Q$
• Dimension: $108$
• Newform subspaces: $20$
• Sturm bound: $1280$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4256 = 2^{5} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4256.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1280\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4256))\).

	Total	New	Old
Modular forms	656	108	548
Cusp forms	625	108	517
Eisenstein series	31	0	31

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

\(2\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(72\)	\(11\)	\(61\)		\(69\)	\(11\)	\(58\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(88\)	\(16\)	\(72\)		\(84\)	\(16\)	\(68\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(86\)	\(16\)	\(70\)		\(82\)	\(16\)	\(66\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(82\)	\(11\)	\(71\)		\(78\)	\(11\)	\(67\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(92\)	\(16\)	\(76\)		\(88\)	\(16\)	\(72\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)		\(76\)	\(11\)	\(65\)		\(72\)	\(11\)	\(61\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)		\(78\)	\(11\)	\(67\)		\(74\)	\(11\)	\(63\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)		\(82\)	\(16\)	\(66\)		\(78\)	\(16\)	\(62\)		\(4\)	\(0\)	\(4\)
Plus space			\(+\)		\(308\)	\(44\)	\(264\)		\(293\)	\(44\)	\(249\)		\(15\)	\(0\)	\(15\)
Minus space			\(-\)		\(348\)	\(64\)	\(284\)		\(332\)	\(64\)	\(268\)		\(16\)	\(0\)	\(16\)

Trace form

108 * q - 8 * q^5 + 108 * q^9 - 8 * q^13 + 24 * q^17 + 132 * q^25 - 8 * q^29 - 40 * q^37 + 24 * q^41 + 56 * q^45 + 108 * q^49 + 88 * q^53 - 40 * q^61 + 48 * q^65 + 96 * q^69 + 24 * q^73 + 108 * q^81 - 48 * q^85 + 24 * q^89 + 96 * q^93 + 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4256))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	7	19
4256.2.a.a	$4256$	$2$	4256.a	1.a	$1$	$1$	$1$	$33.984$	\(\Q\)	None	✓	✓			4256.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}-4q^{13}+6q^{17}+\cdots\)
4256.2.a.b	$4256$	$2$	4256.a	1.a	$1$	$1$	$1$	$33.984$	\(\Q\)	None	✓	✓			4256.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-3q^{9}-4q^{13}+6q^{17}+\cdots\)
4256.2.a.c	$4256$	$2$	4256.a	1.a	$1$	$2$	$2$	$33.984$	\(\Q(\sqrt{5}) \)	None	✓	✓			4256.2.a.c	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+\beta q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots\)
4256.2.a.d	$4256$	$2$	4256.a	1.a	$1$	$2$	$2$	$33.984$	\(\Q(\sqrt{5}) \)	None	✓	✓			4256.2.a.c	$1$	$0$	\(0\)	\(3\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+\beta q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
4256.2.a.e	$4256$	$2$	4256.a	1.a	$1$	$4$	$4$	$33.984$	4.4.2624.1	None	✓	✓			4256.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
4256.2.a.f	$4256$	$2$	4256.a	1.a	$1$	$4$	$4$	$33.984$	4.4.2624.1	None	✓	✓			4256.2.a.e	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
4256.2.a.g	$4256$	$2$	4256.a	1.a	$1$	$5$	$5$	$33.984$	5.5.1730752.1	None	✓	✓			4256.2.a.g	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
4256.2.a.h	$4256$	$2$	4256.a	1.a	$1$	$5$	$5$	$33.984$	5.5.1730752.1	None	✓	✓			4256.2.a.g	$1$	$1$	\(0\)	\(2\)	\(-6\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}-q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
4256.2.a.i	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.41027408.1	None	✓	✓	✓		4256.2.a.i	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
4256.2.a.j	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		4256.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4256.2.a.k	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.60663248.1	None	✓	✓	✓		4256.2.a.k	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+q^{7}+(1-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
4256.2.a.l	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			4256.2.a.j	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4256.2.a.m	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.60663248.1	None	✓	✓			4256.2.a.k	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{5}q^{5}-q^{7}+(1-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
4256.2.a.n	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.41027408.1	None	✓	✓			4256.2.a.i	$1$	$0$	\(0\)	\(3\)	\(3\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
4256.2.a.o	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			4256.2.a.o	$1$	$0$	\(0\)	\(-7\)	\(5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1+\beta _{3})q^{5}-q^{7}+\cdots\)
4256.2.a.p	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		4256.2.a.p	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
4256.2.a.q	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			4256.2.a.p	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}-q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
4256.2.a.r	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		4256.2.a.o	$1$	$0$	\(0\)	\(7\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
4256.2.a.s	$4256$	$2$	4256.a	1.a	$1$	$10$	$10$	$33.984$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		4256.2.a.s	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{5}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
4256.2.a.t	$4256$	$2$	4256.a	1.a	$1$	$10$	$10$	$33.984$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		4256.2.a.s	$1$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{5}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4256))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4256)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2128))\)\(^{\oplus 2}\)