Space of modular forms of level 1014 and weight 2

• Label: 1014.2
• Level: 1014
• Weight: 2
• Dimension: 7013
• Nonzero newspaces: 12
• Sturm bound: 113568
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(113568\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1014))\).

	Total	New	Old
Modular forms	29304	7013	22291
Cusp forms	27481	7013	20468
Eisenstein series	1823	0	1823

Trace form

7013 * q - q^2 - q^3 - q^4 - 6 * q^5 - q^6 + 8 * q^7 + 11 * q^8 + 7 * q^9 + 54 * q^10 + 36 * q^11 + 7 * q^12 + 48 * q^13 + 40 * q^14 + 42 * q^15 + 15 * q^16 + 42 * q^17 + 11 * q^18 + 92 * q^19 + 6 * q^20 + 48 * q^21 - 12 * q^22 + 24 * q^23 - q^24 + 29 * q^25 + 71 * q^27 - 8 * q^28 + 30 * q^29 - 54 * q^30 + 16 * q^31 - q^32 - 36 * q^33 - 18 * q^34 - 49 * q^36 - 26 * q^37 - 20 * q^38 - 44 * q^39 - 6 * q^40 - 30 * q^41 - 80 * q^42 + 20 * q^43 - 12 * q^44 - 114 * q^45 - 24 * q^46 - q^48 - 41 * q^49 - 19 * q^50 + 30 * q^51 + 6 * q^52 + 90 * q^53 + 71 * q^54 + 168 * q^55 + 40 * q^56 + 108 * q^57 + 78 * q^58 + 132 * q^59 + 42 * q^60 + 94 * q^61 + 112 * q^62 + 120 * q^63 + 11 * q^64 + 102 * q^65 + 84 * q^66 + 140 * q^67 - 6 * q^68 + 72 * q^69 + 96 * q^70 + 24 * q^71 + 47 * q^72 + 86 * q^73 + 118 * q^74 + 25 * q^75 + 92 * q^76 + 192 * q^77 + 60 * q^78 + 208 * q^79 + 6 * q^80 - 41 * q^81 + 162 * q^82 + 60 * q^83 + 48 * q^84 + 192 * q^85 + 52 * q^86 + 18 * q^87 - 12 * q^88 + 150 * q^89 + 42 * q^90 + 104 * q^91 + 72 * q^92 + 48 * q^93 + 192 * q^94 + 72 * q^95 - q^96 + 190 * q^97 + 39 * q^98 - 84 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)

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
1014.2.a	\(\chi_{1014}(1, \cdot)\)	1014.2.a.a	1	1
		1014.2.a.b	1
		1014.2.a.c	1
		1014.2.a.d	1
		1014.2.a.e	1
		1014.2.a.f	1
		1014.2.a.g	1
		1014.2.a.h	2
		1014.2.a.i	2
		1014.2.a.j	2
		1014.2.a.k	2
		1014.2.a.l	3
		1014.2.a.m	3
		1014.2.a.n	3
		1014.2.a.o	3
1014.2.b	\(\chi_{1014}(337, \cdot)\)	1014.2.b.a	2	1
		1014.2.b.b	2
		1014.2.b.c	2
		1014.2.b.d	4
		1014.2.b.e	4
		1014.2.b.f	6
		1014.2.b.g	6
1014.2.e	\(\chi_{1014}(529, \cdot)\)	1014.2.e.a	2	2
		1014.2.e.b	2
		1014.2.e.c	2
		1014.2.e.d	2
		1014.2.e.e	2
		1014.2.e.f	2
		1014.2.e.g	4
		1014.2.e.h	4
		1014.2.e.i	4
		1014.2.e.j	4
		1014.2.e.k	6
		1014.2.e.l	6
		1014.2.e.m	6
		1014.2.e.n	6
1014.2.g	\(\chi_{1014}(239, \cdot)\)	1014.2.g.a	8	2
		1014.2.g.b	12
		1014.2.g.c	16
		1014.2.g.d	16
		1014.2.g.e	48
1014.2.i	\(\chi_{1014}(361, \cdot)\)	1014.2.i.a	4	2
		1014.2.i.b	4
		1014.2.i.c	4
		1014.2.i.d	4
		1014.2.i.e	4
		1014.2.i.f	4
		1014.2.i.g	12
		1014.2.i.h	12
1014.2.k	\(\chi_{1014}(89, \cdot)\)	n/a	208	4
1014.2.m	\(\chi_{1014}(79, \cdot)\)	n/a	336	12
1014.2.p	\(\chi_{1014}(25, \cdot)\)	n/a	360	12
1014.2.q	\(\chi_{1014}(55, \cdot)\)	n/a	720	24
1014.2.r	\(\chi_{1014}(5, \cdot)\)	n/a	1488	24
1014.2.u	\(\chi_{1014}(43, \cdot)\)	n/a	768	24
1014.2.x	\(\chi_{1014}(11, \cdot)\)	n/a	2880	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 1}\)