Space of modular forms of level 6015, weight 2, and trivial character

• Label: 6015.2.a
• Level: $6015$
• Weight: $2$
• Character orbit: 6015.a
• Rep. character: $\chi_{6015}(1,\cdot)$
• Character field: $\Q$
• Dimension: $267$
• Newform subspaces: $9$
• Sturm bound: $1608$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1608\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6015))\).

	Total	New	Old
Modular forms	808	267	541
Cusp forms	801	267	534
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.

\(3\)	\(5\)	\(401\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(36\)
\(+\)	\(+\)	\(-\)	$-$	\(31\)
\(+\)	\(-\)	\(+\)	$-$	\(36\)
\(+\)	\(-\)	\(-\)	$+$	\(29\)
\(-\)	\(+\)	\(+\)	$-$	\(39\)
\(-\)	\(+\)	\(-\)	$+$	\(28\)
\(-\)	\(-\)	\(+\)	$+$	\(23\)
\(-\)	\(-\)	\(-\)	$-$	\(45\)
Plus space			\(+\)	\(116\)
Minus space			\(-\)	\(151\)

Trace form

\( 267 q - 3 q^{2} + 3 q^{3} + 269 q^{4} - q^{5} + q^{6} - 15 q^{8} + 267 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6015))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	401
6015.2.a.a	$6015$	$2$	6015.a	1.a	$1$	$2$	$2$	$48.030$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(2\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+(2-2\beta )q^{7}+\cdots\)
6015.2.a.b	$6015$	$2$	6015.a	1.a	$1$	$23$	$23$	$48.030$		None	✓	$1$	$1$	\(-5\)	\(23\)	\(23\)	\(-16\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
6015.2.a.c	$6015$	$2$	6015.a	1.a	$1$	$28$	$28$	$48.030$		None	✓	$1$	$1$	\(-1\)	\(28\)	\(-28\)	\(-20\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
6015.2.a.d	$6015$	$2$	6015.a	1.a	$1$	$29$	$29$	$48.030$		None	✓	$1$	$1$	\(-1\)	\(-29\)	\(29\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
6015.2.a.e	$6015$	$2$	6015.a	1.a	$1$	$31$	$31$	$48.030$		None	✓	$1$	$0$	\(6\)	\(-31\)	\(-31\)	\(-4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6015.2.a.f	$6015$	$2$	6015.a	1.a	$1$	$36$	$36$	$48.030$		None	✓	$1$	$1$	\(-7\)	\(-36\)	\(-36\)	\(2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6015.2.a.g	$6015$	$2$	6015.a	1.a	$1$	$36$	$36$	$48.030$		None	✓	$1$	$0$	\(0\)	\(-36\)	\(36\)	\(-4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
6015.2.a.h	$6015$	$2$	6015.a	1.a	$1$	$39$	$39$	$48.030$		None	✓	$1$	$0$	\(0\)	\(39\)	\(-39\)	\(22\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
6015.2.a.i	$6015$	$2$	6015.a	1.a	$1$	$43$	$43$	$48.030$		None	✓	$1$	$0$	\(3\)	\(43\)	\(43\)	\(14\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1203))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 2}\)