Space of modular forms of level 1444 and weight 1

• Label: 1444.1
• Level: 1444
• Weight: 1
• Dimension: 62
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 129960
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(129960\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1444))\).

	Total	New	Old
Modular forms	1324	531	793
Cusp forms	64	62	2
Eisenstein series	1260	469	791

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	44	0	18	0

Trace form

\( 62 q + q^{5} + q^{7} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1444))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
1444.1.b	\(\chi_{1444}(723, \cdot)\)	1444.1.b.a	2	1
		1444.1.b.b	2
1444.1.c	\(\chi_{1444}(721, \cdot)\)	1444.1.c.a	2	1
1444.1.g	\(\chi_{1444}(1151, \cdot)\)	1444.1.g.a	4	2
		1444.1.g.b	4
1444.1.h	\(\chi_{1444}(69, \cdot)\)	1444.1.h.a	2	2
		1444.1.h.b	4
1444.1.j	\(\chi_{1444}(333, \cdot)\)	1444.1.j.a	6	6
		1444.1.j.b	12
1444.1.l	\(\chi_{1444}(99, \cdot)\)	1444.1.l.a	12	6
		1444.1.l.b	12
1444.1.o	\(\chi_{1444}(37, \cdot)\)	None	0	18
1444.1.p	\(\chi_{1444}(39, \cdot)\)	None	0	18
1444.1.r	\(\chi_{1444}(65, \cdot)\)	None	0	36
1444.1.s	\(\chi_{1444}(7, \cdot)\)	None	0	36
1444.1.v	\(\chi_{1444}(23, \cdot)\)	None	0	108
1444.1.x	\(\chi_{1444}(13, \cdot)\)	None	0	108

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1444))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1444)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)