Space of modular forms of level 6013, weight 2, and trivial character

• Label: 6013.2.a
• Level: $6013$
• Weight: $2$
• Character orbit: 6013.a
• Rep. character: $\chi_{6013}(1,\cdot)$
• Character field: $\Q$
• Dimension: $429$
• Newform subspaces: $6$
• Sturm bound: $1146$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1146\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6013))\).

	Total	New	Old
Modular forms	574	429	145
Cusp forms	571	429	142
Eisenstein series	3	0	3

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

\(7\)	\(859\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(104\)
\(+\)	\(-\)	$-$	\(111\)
\(-\)	\(+\)	$-$	\(110\)
\(-\)	\(-\)	$+$	\(104\)
Plus space		\(+\)	\(208\)
Minus space		\(-\)	\(221\)

Trace form

\( 429 q - q^{2} + 4 q^{3} + 431 q^{4} - 2 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} + 433 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6013))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	859
6013.2.a.a	$6013$	$2$	6013.a	1.a	$1$	$1$	$1$	$48.014$	\(\Q\)	None	✓	$1$	$2$	\(-2\)	\(-2\)	\(-1\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
6013.2.a.b	$6013$	$2$	6013.a	1.a	$1$	$1$	$1$	$48.014$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}-2q^{9}+\cdots\)
6013.2.a.c	$6013$	$2$	6013.a	1.a	$1$	$104$	$104$	$48.014$		None	✓	$1$	$1$	\(-19\)	\(-26\)	\(2\)	\(-104\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6013.2.a.d	$6013$	$2$	6013.a	1.a	$1$	$104$	$104$	$48.014$		None	✓	$1$	$1$	\(-17\)	\(-34\)	\(-46\)	\(104\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6013.2.a.e	$6013$	$2$	6013.a	1.a	$1$	$109$	$109$	$48.014$		None	✓	$1$	$0$	\(19\)	\(38\)	\(43\)	\(109\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6013.2.a.f	$6013$	$2$	6013.a	1.a	$1$	$110$	$110$	$48.014$		None	✓	$1$	$0$	\(16\)	\(29\)	\(0\)	\(-110\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(859))\)\(^{\oplus 2}\)