Space of modular forms of level 6026, weight 2, and trivial character

• Label: 6026.2.a
• Level: $6026$
• Weight: $2$
• Character orbit: 6026.a
• Rep. character: $\chi_{6026}(1,\cdot)$
• Character field: $\Q$
• Dimension: $241$
• Newform subspaces: $13$
• Sturm bound: $1584$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(1584\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6026))\).

	Total	New	Old
Modular forms	796	241	555
Cusp forms	789	241	548
Eisenstein series	7	0	7

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

\(2\)	\(23\)	\(131\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(25\)
\(+\)	\(+\)	\(-\)	$-$	\(36\)
\(+\)	\(-\)	\(+\)	$-$	\(34\)
\(+\)	\(-\)	\(-\)	$+$	\(25\)
\(-\)	\(+\)	\(+\)	$-$	\(37\)
\(-\)	\(+\)	\(-\)	$+$	\(23\)
\(-\)	\(-\)	\(+\)	$+$	\(20\)
\(-\)	\(-\)	\(-\)	$-$	\(41\)
Plus space			\(+\)	\(93\)
Minus space			\(-\)	\(148\)

Trace form

\( 241 q + q^{2} + 241 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} + q^{8} + 257 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\) 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	23	131
6026.2.a.a	$6026$	$2$	6026.a	1.a	$1$	$1$	$1$	$48.118$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
6026.2.a.b	$6026$	$2$	6026.a	1.a	$1$	$1$	$1$	$48.118$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
6026.2.a.c	$6026$	$2$	6026.a	1.a	$1$	$1$	$1$	$48.118$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\)
6026.2.a.d	$6026$	$2$	6026.a	1.a	$1$	$1$	$1$	$48.118$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
6026.2.a.e	$6026$	$2$	6026.a	1.a	$1$	$2$	$2$	$48.118$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(2\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots\)
6026.2.a.f	$6026$	$2$	6026.a	1.a	$1$	$20$	$20$	$48.118$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(20\)	\(-5\)	\(-6\)	\(-12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
6026.2.a.g	$6026$	$2$	6026.a	1.a	$1$	$21$	$21$	$48.118$		None	✓	$1$	$1$	\(21\)	\(0\)	\(-13\)	\(-18\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
6026.2.a.h	$6026$	$2$	6026.a	1.a	$1$	$24$	$24$	$48.118$		None	✓	$1$	$1$	\(-24\)	\(-1\)	\(-1\)	\(-7\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6026.2.a.i	$6026$	$2$	6026.a	1.a	$1$	$25$	$25$	$48.118$		None	✓	$1$	$1$	\(-25\)	\(-4\)	\(-3\)	\(-11\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
6026.2.a.j	$6026$	$2$	6026.a	1.a	$1$	$33$	$33$	$48.118$		None	✓	$1$	$0$	\(-33\)	\(3\)	\(-4\)	\(11\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
6026.2.a.k	$6026$	$2$	6026.a	1.a	$1$	$35$	$35$	$48.118$		None	✓	$1$	$0$	\(35\)	\(-3\)	\(10\)	\(14\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
6026.2.a.l	$6026$	$2$	6026.a	1.a	$1$	$36$	$36$	$48.118$		None	✓	$1$	$0$	\(-36\)	\(4\)	\(1\)	\(13\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6026.2.a.m	$6026$	$2$	6026.a	1.a	$1$	$41$	$41$	$48.118$		None	✓	$1$	$0$	\(41\)	\(4\)	\(9\)	\(12\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6026))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(262))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3013))\)\(^{\oplus 2}\)