Space of modular forms of level 4012 and weight 2

• Label: 4012.2
• Level: 4012
• Weight: 2
• Dimension: 288414
• Nonzero newspaces: 20
• Sturm bound: 2004480

Defining parameters

Level:	\( N \)	=	\( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(2004480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4012))\).

	Total	New	Old
Modular forms	505760	291830	213930
Cusp forms	496481	288414	208067
Eisenstein series	9279	3416	5863

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4012))\)

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
4012.2.a	\(\chi_{4012}(1, \cdot)\)	4012.2.a.a	1	1
		4012.2.a.b	1
		4012.2.a.c	1
		4012.2.a.d	2
		4012.2.a.e	2
		4012.2.a.f	3
		4012.2.a.g	12
		4012.2.a.h	15
		4012.2.a.i	18
		4012.2.a.j	21
4012.2.b	\(\chi_{4012}(237, \cdot)\)	4012.2.b.a	40	1
		4012.2.b.b	46
4012.2.e	\(\chi_{4012}(3775, \cdot)\)	n/a	480	1
4012.2.f	\(\chi_{4012}(4011, \cdot)\)	n/a	536	1
4012.2.j	\(\chi_{4012}(1415, \cdot)\)	n/a	1072	2
4012.2.k	\(\chi_{4012}(1653, \cdot)\)	n/a	172	2
4012.2.n	\(\chi_{4012}(1181, \cdot)\)	n/a	352	4
4012.2.o	\(\chi_{4012}(943, \cdot)\)	n/a	2144	4
4012.2.q	\(\chi_{4012}(827, \cdot)\)	n/a	4176	8
4012.2.t	\(\chi_{4012}(589, \cdot)\)	n/a	720	8
4012.2.u	\(\chi_{4012}(137, \cdot)\)	n/a	2240	28
4012.2.x	\(\chi_{4012}(67, \cdot)\)	n/a	15008	28
4012.2.y	\(\chi_{4012}(103, \cdot)\)	n/a	13440	28
4012.2.bb	\(\chi_{4012}(169, \cdot)\)	n/a	2520	28
4012.2.bd	\(\chi_{4012}(21, \cdot)\)	n/a	5040	56
4012.2.be	\(\chi_{4012}(47, \cdot)\)	n/a	30016	56
4012.2.bh	\(\chi_{4012}(43, \cdot)\)	n/a	60032	112
4012.2.bi	\(\chi_{4012}(9, \cdot)\)	n/a	10080	112
4012.2.bk	\(\chi_{4012}(37, \cdot)\)	n/a	20160	224
4012.2.bn	\(\chi_{4012}(3, \cdot)\)	n/a	120064	224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2006))\)\(^{\oplus 2}\)