Space of modular forms of level 8028 and weight 2

• Label: 8028.2
• Level: 8028
• Weight: 2
• Dimension: 824704
• Nonzero newspaces: 40
• Sturm bound: 7160832

Defining parameters

Level:	\( N \)	=	\( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(7160832\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8028))\).

	Total	New	Old
Modular forms	1799088	828684	970404
Cusp forms	1781329	824704	956625
Eisenstein series	17759	3980	13779

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8028))\)

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

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
8028.2.a	\(\chi_{8028}(1, \cdot)\)	8028.2.a.a	1	1
		8028.2.a.b	1
		8028.2.a.c	1
		8028.2.a.d	1
		8028.2.a.e	1
		8028.2.a.f	1
		8028.2.a.g	2
		8028.2.a.h	2
		8028.2.a.i	5
		8028.2.a.j	7
		8028.2.a.k	8
		8028.2.a.l	8
		8028.2.a.m	11
		8028.2.a.n	11
		8028.2.a.o	16
		8028.2.a.p	16
8028.2.b	\(\chi_{8028}(1783, \cdot)\)	n/a	558	1
8028.2.c	\(\chi_{8028}(2231, \cdot)\)	n/a	444	1
8028.2.h	\(\chi_{8028}(4013, \cdot)\)	8028.2.h.a	76	1
8028.2.i	\(\chi_{8028}(2677, \cdot)\)	n/a	444	2
8028.2.j	\(\chi_{8028}(5089, \cdot)\)	n/a	448	2
8028.2.k	\(\chi_{8028}(2269, \cdot)\)	n/a	186	2
8028.2.l	\(\chi_{8028}(4945, \cdot)\)	n/a	448	2
8028.2.o	\(\chi_{8028}(1823, \cdot)\)	n/a	2680	2
8028.2.p	\(\chi_{8028}(2191, \cdot)\)	n/a	2680	2
8028.2.s	\(\chi_{8028}(1337, \cdot)\)	n/a	448	2
8028.2.t	\(\chi_{8028}(4421, \cdot)\)	n/a	448	2
8028.2.y	\(\chi_{8028}(1601, \cdot)\)	n/a	148	2
8028.2.z	\(\chi_{8028}(7399, \cdot)\)	n/a	1116	2
8028.2.ba	\(\chi_{8028}(4499, \cdot)\)	n/a	896	2
8028.2.bf	\(\chi_{8028}(4907, \cdot)\)	n/a	2664	2
8028.2.bg	\(\chi_{8028}(4459, \cdot)\)	n/a	2680	2
8028.2.bh	\(\chi_{8028}(1967, \cdot)\)	n/a	2680	2
8028.2.bi	\(\chi_{8028}(2047, \cdot)\)	n/a	2680	2
8028.2.bl	\(\chi_{8028}(4277, \cdot)\)	n/a	448	2
8028.2.bo	\(\chi_{8028}(253, \cdot)\)	n/a	3384	36
8028.2.bp	\(\chi_{8028}(125, \cdot)\)	n/a	2736	36
8028.2.bu	\(\chi_{8028}(251, \cdot)\)	n/a	16128	36
8028.2.bv	\(\chi_{8028}(91, \cdot)\)	n/a	20088	36
8028.2.bw	\(\chi_{8028}(121, \cdot)\)	n/a	16128	72
8028.2.bx	\(\chi_{8028}(37, \cdot)\)	n/a	6696	72
8028.2.by	\(\chi_{8028}(25, \cdot)\)	n/a	16128	72
8028.2.bz	\(\chi_{8028}(49, \cdot)\)	n/a	16128	72
8028.2.cc	\(\chi_{8028}(113, \cdot)\)	n/a	16128	72
8028.2.cf	\(\chi_{8028}(403, \cdot)\)	n/a	96480	72
8028.2.cg	\(\chi_{8028}(203, \cdot)\)	n/a	96480	72
8028.2.ch	\(\chi_{8028}(103, \cdot)\)	n/a	96480	72
8028.2.ci	\(\chi_{8028}(119, \cdot)\)	n/a	96480	72
8028.2.cn	\(\chi_{8028}(143, \cdot)\)	n/a	32256	72
8028.2.co	\(\chi_{8028}(235, \cdot)\)	n/a	40176	72
8028.2.cp	\(\chi_{8028}(161, \cdot)\)	n/a	5328	72
8028.2.cu	\(\chi_{8028}(5, \cdot)\)	n/a	16128	72
8028.2.cv	\(\chi_{8028}(209, \cdot)\)	n/a	16128	72
8028.2.cy	\(\chi_{8028}(67, \cdot)\)	n/a	96480	72
8028.2.cz	\(\chi_{8028}(47, \cdot)\)	n/a	96480	72

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(892))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4014))\)\(^{\oplus 2}\)