Space of modular forms of level 6014, weight 2, and trivial character

• Label: 6014.2.a
• Level: $6014$
• Weight: $2$
• Character orbit: 6014.a
• Rep. character: $\chi_{6014}(1,\cdot)$
• Character field: $\Q$
• Dimension: $239$
• Newform subspaces: $12$
• Sturm bound: $1568$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1568\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6014))\).

	Total	New	Old
Modular forms	788	239	549
Cusp forms	781	239	542
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.

\(2\)	\(31\)	\(97\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(26\)
\(+\)	\(+\)	\(-\)	$-$	\(34\)
\(+\)	\(-\)	\(+\)	$-$	\(38\)
\(+\)	\(-\)	\(-\)	$+$	\(22\)
\(-\)	\(+\)	\(+\)	$-$	\(33\)
\(-\)	\(+\)	\(-\)	$+$	\(27\)
\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(-\)	\(-\)	$-$	\(38\)
Plus space			\(+\)	\(96\)
Minus space			\(-\)	\(143\)

Trace form

\( 239 q - q^{2} - 4 q^{3} + 239 q^{4} + 6 q^{5} + 4 q^{6} - q^{8} + 235 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\) 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	31	97
6014.2.a.a	$6014$	$2$	6014.a	1.a	$1$	$1$	$1$	$48.022$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
6014.2.a.b	$6014$	$2$	6014.a	1.a	$1$	$1$	$1$	$48.022$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots\)
6014.2.a.c	$6014$	$2$	6014.a	1.a	$1$	$2$	$2$	$48.022$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2\beta q^{3}+q^{4}+(2+\beta )q^{5}-2\beta q^{6}+\cdots\)
6014.2.a.d	$6014$	$2$	6014.a	1.a	$1$	$5$	$5$	$48.022$	5.5.380224.1	None	✓	$1$	$0$	\(5\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
6014.2.a.e	$6014$	$2$	6014.a	1.a	$1$	$21$	$21$	$48.022$		None	✓	$1$	$1$	\(21\)	\(-10\)	\(-10\)	\(-11\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
6014.2.a.f	$6014$	$2$	6014.a	1.a	$1$	$22$	$22$	$48.022$		None	✓	$1$	$1$	\(-22\)	\(0\)	\(0\)	\(-11\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
6014.2.a.g	$6014$	$2$	6014.a	1.a	$1$	$26$	$26$	$48.022$		None	✓	$1$	$1$	\(-26\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6014.2.a.h	$6014$	$2$	6014.a	1.a	$1$	$26$	$26$	$48.022$		None	✓	$1$	$1$	\(26\)	\(-10\)	\(-8\)	\(-9\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
6014.2.a.i	$6014$	$2$	6014.a	1.a	$1$	$28$	$28$	$48.022$		None	✓	$1$	$0$	\(28\)	\(12\)	\(10\)	\(13\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
6014.2.a.j	$6014$	$2$	6014.a	1.a	$1$	$32$	$32$	$48.022$		None	✓	$1$	$0$	\(-32\)	\(-2\)	\(0\)	\(5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6014.2.a.k	$6014$	$2$	6014.a	1.a	$1$	$37$	$37$	$48.022$		None	✓	$1$	$0$	\(37\)	\(9\)	\(9\)	\(19\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
6014.2.a.l	$6014$	$2$	6014.a	1.a	$1$	$38$	$38$	$48.022$		None	✓	$1$	$0$	\(-38\)	\(-2\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(97))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(194))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3007))\)\(^{\oplus 2}\)