Space of modular forms of level 6256, weight 2, and trivial character

• Label: 6256.2.a
• Level: $6256$
• Weight: $2$
• Character orbit: 6256.a
• Rep. character: $\chi_{6256}(1,\cdot)$
• Character field: $\Q$
• Dimension: $176$
• Newform subspaces: $36$
• Sturm bound: $1728$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 6256 = 2^{4} \cdot 17 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6256.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 36 \)
Sturm bound:			\(1728\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6256))\).

	Total	New	Old
Modular forms	876	176	700
Cusp forms	853	176	677
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.

\(2\)	\(17\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(22\)
\(+\)	\(+\)	\(-\)	$-$	\(22\)
\(+\)	\(-\)	\(+\)	$-$	\(22\)
\(+\)	\(-\)	\(-\)	$+$	\(22\)
\(-\)	\(+\)	\(+\)	$-$	\(24\)
\(-\)	\(+\)	\(-\)	$+$	\(20\)
\(-\)	\(-\)	\(+\)	$+$	\(17\)
\(-\)	\(-\)	\(-\)	$-$	\(27\)
Plus space			\(+\)	\(81\)
Minus space			\(-\)	\(95\)

Trace form

\( 176 q - 4 q^{3} - 8 q^{7} + 176 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6256))\) 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	17	23
6256.2.a.a	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{7}+6q^{9}+2q^{11}+2q^{13}+\cdots\)
6256.2.a.b	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+6q^{9}+3q^{13}-6q^{15}+\cdots\)
6256.2.a.c	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-3q^{7}-2q^{9}-6q^{11}+\cdots\)
6256.2.a.d	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}-2q^{9}-q^{13}+\cdots\)
6256.2.a.e	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-q^{7}-2q^{9}-6q^{11}+\cdots\)
6256.2.a.f	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{9}+6q^{13}+q^{17}-4q^{19}+\cdots\)
6256.2.a.g	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
6256.2.a.h	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6256.2.a.i	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{9}-6q^{13}+4q^{15}+\cdots\)
6256.2.a.j	$6256$	$2$	6256.a	1.a	$1$	$1$	$1$	$49.954$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{7}+6q^{9}-4q^{11}-q^{13}+\cdots\)
6256.2.a.k	$6256$	$2$	6256.a	1.a	$1$	$2$	$2$	$49.954$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}-2q^{9}+\cdots\)
6256.2.a.l	$6256$	$2$	6256.a	1.a	$1$	$2$	$2$	$49.954$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(2-\beta )q^{7}-2q^{9}+(-2+\cdots)q^{11}+\cdots\)
6256.2.a.m	$6256$	$2$	6256.a	1.a	$1$	$2$	$2$	$49.954$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(6\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+(-2+\beta )q^{7}-2q^{9}+\cdots\)
6256.2.a.n	$6256$	$2$	6256.a	1.a	$1$	$2$	$2$	$49.954$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{3}-q^{5}+(1+\beta )q^{7}+2q^{9}+\cdots\)
6256.2.a.o	$6256$	$2$	6256.a	1.a	$1$	$2$	$2$	$49.954$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-2\beta )q^{5}+(3-3\beta )q^{7}-2q^{9}+\cdots\)
6256.2.a.p	$6256$	$2$	6256.a	1.a	$1$	$2$	$2$	$49.954$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(4\)	\(-7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+2\beta )q^{5}+(-3-\beta )q^{7}-2q^{9}+\cdots\)
6256.2.a.q	$6256$	$2$	6256.a	1.a	$1$	$3$	$3$	$49.954$	3.3.169.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(2+\beta _{2})q^{7}-3q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
6256.2.a.r	$6256$	$2$	6256.a	1.a	$1$	$3$	$3$	$49.954$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
6256.2.a.s	$6256$	$2$	6256.a	1.a	$1$	$3$	$3$	$49.954$	3.3.257.1	None	✓	$1$	$1$	\(0\)	\(6\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
6256.2.a.t	$6256$	$2$	6256.a	1.a	$1$	$4$	$4$	$49.954$	4.4.7625.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-5\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-1-\beta _{1})q^{7}+2q^{9}+\cdots\)
6256.2.a.u	$6256$	$2$	6256.a	1.a	$1$	$5$	$5$	$49.954$	5.5.4197836.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots\)
6256.2.a.v	$6256$	$2$	6256.a	1.a	$1$	$6$	$6$	$49.954$	6.6.100211904.1	None	✓	$1$	$1$	\(0\)	\(-6\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
6256.2.a.w	$6256$	$2$	6256.a	1.a	$1$	$6$	$6$	$49.954$	6.6.176217004.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-9\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(-2-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
6256.2.a.x	$6256$	$2$	6256.a	1.a	$1$	$6$	$6$	$49.954$	6.6.298607104.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
6256.2.a.y	$6256$	$2$	6256.a	1.a	$1$	$7$	$7$	$49.954$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+(-1-\beta _{2}+\beta _{4}+\beta _{6})q^{5}+\cdots\)
6256.2.a.z	$6256$	$2$	6256.a	1.a	$1$	$7$	$7$	$49.954$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+(\beta _{1}+\beta _{4})q^{5}+(1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
6256.2.a.ba	$6256$	$2$	6256.a	1.a	$1$	$8$	$8$	$49.954$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(9\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots\)
6256.2.a.bb	$6256$	$2$	6256.a	1.a	$1$	$9$	$9$	$49.954$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(\beta _{1}+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
6256.2.a.bc	$6256$	$2$	6256.a	1.a	$1$	$9$	$9$	$49.954$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(7\)	\(-3\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{3}+(1-\beta _{5})q^{5}+\beta _{3}q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
6256.2.a.bd	$6256$	$2$	6256.a	1.a	$1$	$9$	$9$	$49.954$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{8}q^{5}+(1+\beta _{6})q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
6256.2.a.be	$6256$	$2$	6256.a	1.a	$1$	$10$	$10$	$49.954$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(1-\beta _{5}-\beta _{6})q^{7}+\cdots\)
6256.2.a.bf	$6256$	$2$	6256.a	1.a	$1$	$11$	$11$	$49.954$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-10\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots\)
6256.2.a.bg	$6256$	$2$	6256.a	1.a	$1$	$12$	$12$	$49.954$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(-9\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(-1+\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
6256.2.a.bh	$6256$	$2$	6256.a	1.a	$1$	$12$	$12$	$49.954$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(5\)	\(9\)		$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-\beta _{4}q^{5}+(1+\beta _{1})q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
6256.2.a.bi	$6256$	$2$	6256.a	1.a	$1$	$12$	$12$	$49.954$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(6\)	\(-5\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{8}q^{5}+\beta _{3}q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
6256.2.a.bj	$6256$	$2$	6256.a	1.a	$1$	$12$	$12$	$49.954$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-6\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1-\beta _{11})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6256))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6256)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(391))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(782))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1564))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3128))\)\(^{\oplus 2}\)