Space of modular forms of level 1441, weight 2, and trivial character

• Label: 1441.2.a
• Level: $1441$
• Weight: $2$
• Character orbit: 1441.a
• Rep. character: $\chi_{1441}(1,\cdot)$
• Character field: $\Q$
• Dimension: $107$
• Newform subspaces: $6$
• Sturm bound: $264$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(264\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1441))\).

	Total	New	Old
Modular forms	134	107	27
Cusp forms	131	107	24
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.

\(11\)	\(131\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(24\)
\(+\)	\(-\)	$-$	\(31\)
\(-\)	\(+\)	$-$	\(29\)
\(-\)	\(-\)	$+$	\(23\)
Plus space		\(+\)	\(47\)
Minus space		\(-\)	\(60\)

Trace form

\( 107 q + q^{2} - 2 q^{3} + 99 q^{4} - 8 q^{5} - 4 q^{6} - 4 q^{7} + 9 q^{8} + 101 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1441))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	131
1441.2.a.a	$1441$	$2$	1441.a	1.a	$1$	$1$	$1$	$11.506$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots\)
1441.2.a.b	$1441$	$2$	1441.a	1.a	$1$	$1$	$1$	$11.506$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(3\)	\(-2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
1441.2.a.c	$1441$	$2$	1441.a	1.a	$1$	$23$	$23$	$11.506$		None	✓	$1$	$1$	\(-7\)	\(-3\)	\(-9\)	\(-12\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
1441.2.a.d	$1441$	$2$	1441.a	1.a	$1$	$23$	$23$	$11.506$		None	✓	$1$	$1$	\(-7\)	\(-3\)	\(-9\)	\(-8\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1441.2.a.e	$1441$	$2$	1441.a	1.a	$1$	$28$	$28$	$11.506$		None	✓	$1$	$0$	\(7\)	\(-2\)	\(3\)	\(7\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1441.2.a.f	$1441$	$2$	1441.a	1.a	$1$	$31$	$31$	$11.506$		None	✓	$1$	$0$	\(6\)	\(4\)	\(8\)	\(4\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1441))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1441)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 2}\)