Space of modular forms of level 6028, weight 2, and trivial character

• Label: 6028.2.a
• Level: $6028$
• Weight: $2$
• Character orbit: 6028.a
• Rep. character: $\chi_{6028}(1,\cdot)$
• Character field: $\Q$
• Dimension: $112$
• Newform subspaces: $6$
• Sturm bound: $1656$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 6028 = 2^{2} \cdot 11 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6028.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1656\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6028))\).

	Total	New	Old
Modular forms	834	112	722
Cusp forms	823	112	711
Eisenstein series	11	0	11

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

\(2\)	\(11\)	\(137\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(27\)
\(-\)	\(+\)	\(-\)	$+$	\(29\)
\(-\)	\(-\)	\(+\)	$+$	\(25\)
\(-\)	\(-\)	\(-\)	$-$	\(31\)
Plus space			\(+\)	\(54\)
Minus space			\(-\)	\(58\)

Trace form

\( 112 q + 4 q^{5} - 4 q^{7} + 116 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6028))\) 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	11	137
6028.2.a.a	$6028$	$2$	6028.a	1.a	$1$	$2$	$2$	$48.134$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-5\)	\(-7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-3+\beta )q^{5}+(-3-\beta )q^{7}+\cdots\)
6028.2.a.b	$6028$	$2$	6028.a	1.a	$1$	$2$	$2$	$48.134$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{5}+(3-\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
6028.2.a.c	$6028$	$2$	6028.a	1.a	$1$	$25$	$25$	$48.134$		None	✓	$1$	$1$	\(0\)	\(-11\)	\(-2\)	\(-9\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
6028.2.a.d	$6028$	$2$	6028.a	1.a	$1$	$27$	$27$	$48.134$		None	✓	$1$	$1$	\(0\)	\(-6\)	\(1\)	\(-14\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
6028.2.a.e	$6028$	$2$	6028.a	1.a	$1$	$27$	$27$	$48.134$		None	✓	$1$	$0$	\(0\)	\(5\)	\(-2\)	\(7\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
6028.2.a.f	$6028$	$2$	6028.a	1.a	$1$	$29$	$29$	$48.134$		None	✓	$1$	$0$	\(0\)	\(14\)	\(9\)	\(14\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(137))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(274))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(548))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1507))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3014))\)\(^{\oplus 2}\)