Space of modular forms of level 4882, weight 2, and trivial character

• Label: 4882.2.a
• Level: $4882$
• Weight: $2$
• Character orbit: 4882.a
• Rep. character: $\chi_{4882}(1,\cdot)$
• Character field: $\Q$
• Dimension: $203$
• Newform subspaces: $7$
• Sturm bound: $1221$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 4882 = 2 \cdot 2441 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4882.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1221\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4882))\).

	Total	New	Old
Modular forms	612	203	409
Cusp forms	609	203	406
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.

\(2\)	\(2441\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(57\)
\(+\)	\(-\)	\(-\)	\(44\)
\(-\)	\(+\)	\(-\)	\(63\)
\(-\)	\(-\)	\(+\)	\(39\)
Plus space		\(+\)	\(96\)
Minus space		\(-\)	\(107\)

Trace form

\( 203 q + q^{2} - 2 q^{3} + 203 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + q^{8} + 199 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4882))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	2441
4882.2.a.a	$4882$	$2$	4882.a	1.a	$1$	$1$	$1$	$38.983$	\(\Q\)	None	✓	✓			4882.2.a.a	$1$	$0$	\(-1\)	\(2\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-4q^{7}+\cdots\)
4882.2.a.b	$4882$	$2$	4882.a	1.a	$1$	$1$	$1$	$38.983$	\(\Q\)	None	✓	✓			4882.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{7}+q^{8}-3q^{9}-4q^{11}+\cdots\)
4882.2.a.c	$4882$	$2$	4882.a	1.a	$1$	$2$	$2$	$38.983$	\(\Q(\sqrt{5}) \)	None	✓	✓			4882.2.a.c	$1$	$1$	\(-2\)	\(2\)	\(6\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2\beta q^{3}+q^{4}+3q^{5}-2\beta q^{6}+\cdots\)
4882.2.a.d	$4882$	$2$	4882.a	1.a	$1$	$38$	$38$	$38.983$		None	✓	✓	✓		4882.2.a.d	$1$	$1$	\(38\)	\(-11\)	\(-20\)	\(-19\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4882.2.a.e	$4882$	$2$	4882.a	1.a	$1$	$43$	$43$	$38.983$		None	✓	✓	✓		4882.2.a.e	$1$	$0$	\(-43\)	\(1\)	\(14\)	\(22\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
4882.2.a.f	$4882$	$2$	4882.a	1.a	$1$	$55$	$55$	$38.983$		None	✓	✓	✓		4882.2.a.f	$1$	$1$	\(-55\)	\(-7\)	\(-18\)	\(-18\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4882.2.a.g	$4882$	$2$	4882.a	1.a	$1$	$63$	$63$	$38.983$		None	✓	✓	✓	✓	4882.2.a.g	$1$	$0$	\(63\)	\(11\)	\(22\)	\(16\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4882))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4882)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2441))\)\(^{\oplus 2}\)