Space of modular forms of level 4425 and weight 2

• Label: 4425.2
• Level: 4425
• Weight: 2
• Dimension: 478494
• Nonzero newspaces: 24
• Sturm bound: 2784000

Defining parameters

Level:	\( N \)	=	\( 4425 = 3 \cdot 5^{2} \cdot 59 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(2784000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4425))\).

	Total	New	Old
Modular forms	702496	483170	219326
Cusp forms	689505	478494	211011
Eisenstein series	12991	4676	8315

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4425))\)

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
4425.2.a	\(\chi_{4425}(1, \cdot)\)	4425.2.a.a	1	1
		4425.2.a.b	1
		4425.2.a.c	1
		4425.2.a.d	1
		4425.2.a.e	1
		4425.2.a.f	1
		4425.2.a.g	1
		4425.2.a.h	1
		4425.2.a.i	1
		4425.2.a.j	1
		4425.2.a.k	1
		4425.2.a.l	1
		4425.2.a.m	1
		4425.2.a.n	1
		4425.2.a.o	2
		4425.2.a.p	2
		4425.2.a.q	2
		4425.2.a.r	2
		4425.2.a.s	2
		4425.2.a.t	2
		4425.2.a.u	2
		4425.2.a.v	3
		4425.2.a.w	3
		4425.2.a.x	3
		4425.2.a.y	4
		4425.2.a.z	4
		4425.2.a.ba	4
		4425.2.a.bb	4
		4425.2.a.bc	4
		4425.2.a.bd	6
		4425.2.a.be	6
		4425.2.a.bf	6
		4425.2.a.bg	6
		4425.2.a.bh	9
		4425.2.a.bi	10
		4425.2.a.bj	10
		4425.2.a.bk	11
		4425.2.a.bl	11
		4425.2.a.bm	13
		4425.2.a.bn	13
		4425.2.a.bo	13
		4425.2.a.bp	13
4425.2.b	\(\chi_{4425}(4249, \cdot)\)	n/a	172	1
4425.2.c	\(\chi_{4425}(4424, \cdot)\)	n/a	356	1
4425.2.h	\(\chi_{4425}(176, \cdot)\)	n/a	374	1
4425.2.i	\(\chi_{4425}(2243, \cdot)\)	n/a	696	2
4425.2.j	\(\chi_{4425}(943, \cdot)\)	n/a	360	2
4425.2.m	\(\chi_{4425}(886, \cdot)\)	n/a	1152	4
4425.2.p	\(\chi_{4425}(1061, \cdot)\)	n/a	2384	4
4425.2.q	\(\chi_{4425}(884, \cdot)\)	n/a	2384	4
4425.2.r	\(\chi_{4425}(709, \cdot)\)	n/a	1168	4
4425.2.w	\(\chi_{4425}(473, \cdot)\)	n/a	4640	8
4425.2.x	\(\chi_{4425}(58, \cdot)\)	n/a	2400	8
4425.2.y	\(\chi_{4425}(76, \cdot)\)	n/a	5320	28
4425.2.z	\(\chi_{4425}(101, \cdot)\)	n/a	10472	28
4425.2.be	\(\chi_{4425}(149, \cdot)\)	n/a	9968	28
4425.2.bf	\(\chi_{4425}(49, \cdot)\)	n/a	5040	28
4425.2.bi	\(\chi_{4425}(43, \cdot)\)	n/a	10080	56
4425.2.bj	\(\chi_{4425}(68, \cdot)\)	n/a	19936	56
4425.2.bk	\(\chi_{4425}(16, \cdot)\)	n/a	33600	112
4425.2.bn	\(\chi_{4425}(4, \cdot)\)	n/a	33600	112
4425.2.bo	\(\chi_{4425}(14, \cdot)\)	n/a	66752	112
4425.2.bp	\(\chi_{4425}(11, \cdot)\)	n/a	66752	112
4425.2.bs	\(\chi_{4425}(13, \cdot)\)	n/a	67200	224
4425.2.bt	\(\chi_{4425}(17, \cdot)\)	n/a	133504	224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4425))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4425)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(295))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(885))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1475))\)\(^{\oplus 2}\)