Space of modular forms of level 6003, weight 2, and trivial character

• Label: 6003.2.a
• Level: $6003$
• Weight: $2$
• Character orbit: 6003.a
• Rep. character: $\chi_{6003}(1,\cdot)$
• Character field: $\Q$
• Dimension: $258$
• Newform subspaces: $23$
• Sturm bound: $1440$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6003.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(1440\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6003))\).

	Total	New	Old
Modular forms	728	258	470
Cusp forms	713	258	455
Eisenstein series	15	0	15

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

\(3\)	\(23\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(22\)
\(+\)	\(+\)	\(-\)	$-$	\(30\)
\(+\)	\(-\)	\(+\)	$-$	\(30\)
\(+\)	\(-\)	\(-\)	$+$	\(22\)
\(-\)	\(+\)	\(+\)	$-$	\(39\)
\(-\)	\(+\)	\(-\)	$+$	\(38\)
\(-\)	\(-\)	\(+\)	$+$	\(35\)
\(-\)	\(-\)	\(-\)	$-$	\(42\)
Plus space			\(+\)	\(117\)
Minus space			\(-\)	\(141\)

Trace form

\( 258 q + 2 q^{2} + 262 q^{4} + 4 q^{7} - 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6003))\) 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	23	29
6003.2.a.a	$6003$	$2$	6003.a	1.a	$1$	$1$	$1$	$47.934$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}-4q^{7}-4q^{11}-5q^{13}+\cdots\)
6003.2.a.b	$6003$	$2$	6003.a	1.a	$1$	$1$	$1$	$47.934$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+4q^{11}+3q^{13}+4q^{16}-3q^{17}+\cdots\)
6003.2.a.c	$6003$	$2$	6003.a	1.a	$1$	$1$	$1$	$47.934$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{5}-3q^{8}-3q^{10}+\cdots\)
6003.2.a.d	$6003$	$2$	6003.a	1.a	$1$	$2$	$2$	$47.934$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+(1+\beta )q^{5}+3q^{8}+(-1+\cdots)q^{10}+\cdots\)
6003.2.a.e	$6003$	$2$	6003.a	1.a	$1$	$2$	$2$	$47.934$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+\beta q^{5}+(-2+\beta )q^{7}+q^{13}+\cdots\)
6003.2.a.f	$6003$	$2$	6003.a	1.a	$1$	$2$	$2$	$47.934$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
6003.2.a.g	$6003$	$2$	6003.a	1.a	$1$	$4$	$4$	$47.934$	4.4.5744.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{4}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
6003.2.a.h	$6003$	$2$	6003.a	1.a	$1$	$5$	$5$	$47.934$	5.5.312617.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(2-\beta _{1})q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
6003.2.a.i	$6003$	$2$	6003.a	1.a	$1$	$7$	$7$	$47.934$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(5\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1+\beta _{4}+\beta _{5})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
6003.2.a.j	$6003$	$2$	6003.a	1.a	$1$	$7$	$7$	$47.934$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(3\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
6003.2.a.k	$6003$	$2$	6003.a	1.a	$1$	$10$	$10$	$47.934$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-6\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(2+\beta _{6})q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
6003.2.a.l	$6003$	$2$	6003.a	1.a	$1$	$10$	$10$	$47.934$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(10\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{7})q^{5}+\cdots\)
6003.2.a.m	$6003$	$2$	6003.a	1.a	$1$	$11$	$11$	$47.934$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(3\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)
6003.2.a.n	$6003$	$2$	6003.a	1.a	$1$	$12$	$12$	$47.934$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(16\)	\(-7\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{4}-\beta _{6}+\beta _{8})q^{4}+(1+\cdots)q^{5}+\cdots\)
6003.2.a.o	$6003$	$2$	6003.a	1.a	$1$	$13$	$13$	$47.934$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-16\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{8})q^{5}+\cdots\)
6003.2.a.p	$6003$	$2$	6003.a	1.a	$1$	$14$	$14$	$47.934$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
6003.2.a.q	$6003$	$2$	6003.a	1.a	$1$	$16$	$16$	$47.934$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-16\)	\(1\)		$-$	$+$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
6003.2.a.r	$6003$	$2$	6003.a	1.a	$1$	$16$	$16$	$47.934$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(13\)		$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}+(1-\beta _{10}+\cdots)q^{7}+\cdots\)
6003.2.a.s	$6003$	$2$	6003.a	1.a	$1$	$20$	$20$	$47.934$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(9\)		$-$	$+$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{14}q^{7}+\cdots\)
6003.2.a.t	$6003$	$2$	6003.a	1.a	$1$	$22$	$22$	$47.934$		None	✓	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(-6\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
6003.2.a.u	$6003$	$2$	6003.a	1.a	$1$	$22$	$22$	$47.934$		None	✓	$1$	$1$	\(3\)	\(0\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6003.2.a.v	$6003$	$2$	6003.a	1.a	$1$	$30$	$30$	$47.934$		None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(10\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
6003.2.a.w	$6003$	$2$	6003.a	1.a	$1$	$30$	$30$	$47.934$		None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(10\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2001))\)\(^{\oplus 2}\)