Space of modular forms of level 6046, weight 2, and trivial character

• Label: 6046.2.a
• Level: $6046$
• Weight: $2$
• Character orbit: 6046.a
• Rep. character: $\chi_{6046}(1,\cdot)$
• Character field: $\Q$
• Dimension: $251$
• Newform subspaces: $7$
• Sturm bound: $1512$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1512\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6046))\).

	Total	New	Old
Modular forms	758	251	507
Cusp forms	755	251	504
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.

\(2\)	\(3023\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(56\)
\(+\)	\(-\)	$-$	\(70\)
\(-\)	\(+\)	$-$	\(69\)
\(-\)	\(-\)	$+$	\(56\)
Plus space		\(+\)	\(112\)
Minus space		\(-\)	\(139\)

Trace form

\( 251 q - q^{2} + 251 q^{4} - 8 q^{7} - q^{8} + 255 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\) 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	3023
6046.2.a.a	$6046$	$2$	6046.a	1.a	$1$	$1$	$1$	$48.278$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}+2q^{7}+\cdots\)
6046.2.a.b	$6046$	$2$	6046.a	1.a	$1$	$1$	$1$	$48.278$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}+2q^{7}+\cdots\)
6046.2.a.c	$6046$	$2$	6046.a	1.a	$1$	$2$	$2$	$48.278$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$2$	\(2\)	\(-3\)	\(-6\)	\(-5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}-3q^{5}+(-1+\cdots)q^{6}+\cdots\)
6046.2.a.d	$6046$	$2$	6046.a	1.a	$1$	$55$	$55$	$48.278$		None	✓	$1$	$1$	\(-55\)	\(-4\)	\(-7\)	\(17\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6046.2.a.e	$6046$	$2$	6046.a	1.a	$1$	$56$	$56$	$48.278$		None	✓	$1$	$1$	\(56\)	\(-18\)	\(-17\)	\(-35\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6046.2.a.f	$6046$	$2$	6046.a	1.a	$1$	$67$	$67$	$48.278$		None	✓	$1$	$0$	\(67\)	\(21\)	\(21\)	\(38\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6046.2.a.g	$6046$	$2$	6046.a	1.a	$1$	$69$	$69$	$48.278$		None	✓	$1$	$0$	\(-69\)	\(0\)	\(13\)	\(-27\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6046))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6046)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3023))\)\(^{\oplus 2}\)