Space of modular forms of level 603, weight 2, and trivial character

• Label: 603.2.a
• Level: $603$
• Weight: $2$
• Character orbit: 603.a
• Rep. character: $\chi_{603}(1,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $12$
• Sturm bound: $136$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(136\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(603))\).

	Total	New	Old
Modular forms	72	28	44
Cusp forms	65	28	37
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.

\(3\)	\(67\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	$-$	\(8\)
\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	$+$	\(7\)
Plus space		\(+\)	\(11\)
Minus space		\(-\)	\(17\)

Trace form

\( 28 q + q^{2} + 25 q^{4} + 6 q^{5} - 2 q^{7} - 3 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(603))\) 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	67
603.2.a.a	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-2q^{5}-2q^{7}+4q^{10}+\cdots\)
603.2.a.b	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+4q^{7}+3q^{8}-2q^{10}+\cdots\)
603.2.a.c	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{5}-3q^{7}+3q^{8}-3q^{10}+\cdots\)
603.2.a.d	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}+4q^{7}-3q^{8}-2q^{10}+\cdots\)
603.2.a.e	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-5q^{7}-3q^{8}+q^{10}+\cdots\)
603.2.a.f	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+6q^{11}+4q^{13}-4q^{16}+\cdots\)
603.2.a.g	$603$	$2$	603.a	1.a	$1$	$2$	$2$	$4.815$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
603.2.a.h	$603$	$2$	603.a	1.a	$1$	$2$	$2$	$4.815$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(3\)	\(0\)	\(6\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+3q^{5}+(1-3\beta )q^{7}+\cdots\)
603.2.a.i	$603$	$2$	603.a	1.a	$1$	$3$	$3$	$4.815$	3.3.148.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
603.2.a.j	$603$	$2$	603.a	1.a	$1$	$4$	$4$	$4.815$	\(\Q(\zeta_{24})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-2\beta _{1}-\beta _{3})q^{5}+\cdots\)
603.2.a.k	$603$	$2$	603.a	1.a	$1$	$5$	$5$	$4.815$	5.5.1025428.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
603.2.a.l	$603$	$2$	603.a	1.a	$1$	$6$	$6$	$4.815$	6.6.2482793472.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(603))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(603)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 2}\)