Space of modular forms of level 1202, weight 2, and trivial character

• Label: 1202.2.a
• Level: $1202$
• Weight: $2$
• Character orbit: 1202.a
• Rep. character: $\chi_{1202}(1,\cdot)$
• Character field: $\Q$
• Dimension: $51$
• Newform subspaces: $6$
• Sturm bound: $301$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1202 = 2 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1202.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(301\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1202))\).

	Total	New	Old
Modular forms	152	51	101
Cusp forms	149	51	98
Eisenstein series	3	0	3

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

\(2\)	\(601\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(12\)
\(+\)	\(-\)	$-$	\(13\)
\(-\)	\(+\)	$-$	\(18\)
\(-\)	\(-\)	$+$	\(8\)
Plus space		\(+\)	\(20\)
Minus space		\(-\)	\(31\)

Trace form

\( 51 q + q^{2} + 51 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{7} + q^{8} + 51 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1202))\) 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	601
1202.2.a.a	$1202$	$2$	1202.a	1.a	$1$	$1$	$1$	$9.598$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
1202.2.a.b	$1202$	$2$	1202.a	1.a	$1$	$2$	$2$	$9.598$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)
1202.2.a.c	$1202$	$2$	1202.a	1.a	$1$	$8$	$8$	$9.598$	8.8.1462785589.1	None	✓	$1$	$1$	\(8\)	\(-3\)	\(-8\)	\(-12\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{6}q^{3}+q^{4}+(-1+\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots\)
1202.2.a.d	$1202$	$2$	1202.a	1.a	$1$	$10$	$10$	$9.598$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-10\)	\(-1\)	\(-1\)	\(-15\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{7}q^{3}+q^{4}+(\beta _{1}-\beta _{8})q^{5}+\cdots\)
1202.2.a.e	$1202$	$2$	1202.a	1.a	$1$	$12$	$12$	$9.598$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-12\)	\(1\)	\(-2\)	\(14\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
1202.2.a.f	$1202$	$2$	1202.a	1.a	$1$	$18$	$18$	$9.598$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(18\)	\(5\)	\(10\)	\(16\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{13})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1202))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1202)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(601))\)\(^{\oplus 2}\)