Space of modular forms of level 6004, weight 2, and trivial character

• Label: 6004.2.a
• Level: $6004$
• Weight: $2$
• Character orbit: 6004.a
• Rep. character: $\chi_{6004}(1,\cdot)$
• Character field: $\Q$
• Dimension: $118$
• Newform subspaces: $8$
• Sturm bound: $1600$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6004.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1600\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6004))\).

	Total	New	Old
Modular forms	806	118	688
Cusp forms	795	118	677
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.

\(2\)	\(19\)	\(79\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(32\)
\(-\)	\(+\)	\(-\)	$+$	\(26\)
\(-\)	\(-\)	\(+\)	$+$	\(27\)
\(-\)	\(-\)	\(-\)	$-$	\(33\)
Plus space			\(+\)	\(53\)
Minus space			\(-\)	\(65\)

Trace form

\( 118 q - 4 q^{3} + 2 q^{5} - 2 q^{7} + 126 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6004))\) 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	19	79
6004.2.a.a	$6004$	$2$	6004.a	1.a	$1$	$1$	$1$	$47.942$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-5q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
6004.2.a.b	$6004$	$2$	6004.a	1.a	$1$	$1$	$1$	$47.942$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-3q^{9}+2q^{11}-4q^{13}+\cdots\)
6004.2.a.c	$6004$	$2$	6004.a	1.a	$1$	$1$	$1$	$47.942$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}-2q^{9}+5q^{13}+\cdots\)
6004.2.a.d	$6004$	$2$	6004.a	1.a	$1$	$8$	$8$	$47.942$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-\beta _{4}q^{7}-3q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6004.2.a.e	$6004$	$2$	6004.a	1.a	$1$	$24$	$24$	$47.942$		None	✓	$1$	$0$	\(0\)	\(1\)	\(9\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
6004.2.a.f	$6004$	$2$	6004.a	1.a	$1$	$25$	$25$	$47.942$		None	✓	$1$	$1$	\(0\)	\(4\)	\(-8\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
6004.2.a.g	$6004$	$2$	6004.a	1.a	$1$	$27$	$27$	$47.942$		None	✓	$1$	$1$	\(0\)	\(-4\)	\(-10\)	\(-8\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
6004.2.a.h	$6004$	$2$	6004.a	1.a	$1$	$31$	$31$	$47.942$		None	✓	$1$	$0$	\(0\)	\(-4\)	\(10\)	\(11\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(158))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(316))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1501))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3002))\)\(^{\oplus 2}\)