Space of modular forms of level 1014 and weight 3

• Label: 1014.3
• Level: 1014
• Weight: 3
• Dimension: 14028
• Nonzero newspaces: 12
• Sturm bound: 170352
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(170352\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1014))\).

	Total	New	Old
Modular forms	57696	14028	43668
Cusp forms	55872	14028	41844
Eisenstein series	1824	0	1824

Trace form

14028 * q - 80 * q^7 - 48 * q^8 - 24 * q^9 - 120 * q^10 - 48 * q^11 + 48 * q^13 + 96 * q^14 + 144 * q^15 + 64 * q^16 + 144 * q^17 + 72 * q^18 + 160 * q^19 + 96 * q^20 - 120 * q^21 - 96 * q^23 + 144 * q^27 + 240 * q^29 + 384 * q^30 + 288 * q^31 + 744 * q^33 + 480 * q^35 + 96 * q^36 + 144 * q^37 - 96 * q^39 - 120 * q^41 - 288 * q^42 - 512 * q^43 - 912 * q^45 - 192 * q^47 - 32 * q^49 - 168 * q^50 - 1248 * q^51 - 72 * q^52 - 960 * q^53 - 720 * q^54 - 912 * q^55 - 384 * q^56 - 792 * q^57 - 648 * q^58 - 336 * q^59 - 192 * q^60 + 312 * q^61 - 288 * q^62 + 600 * q^63 + 180 * q^65 + 192 * q^66 + 832 * q^67 + 48 * q^68 + 1416 * q^69 + 864 * q^70 + 672 * q^71 + 384 * q^72 + 1024 * q^73 + 312 * q^74 + 720 * q^75 - 320 * q^76 + 216 * q^78 - 672 * q^79 + 192 * q^80 + 360 * q^81 - 1320 * q^82 - 1008 * q^83 - 336 * q^84 - 1656 * q^85 - 384 * q^86 - 1392 * q^87 - 864 * q^89 + 104 * q^91 + 192 * q^92 - 1320 * q^93 + 960 * q^94 + 960 * q^95 + 2640 * q^97 + 768 * q^98 + 1224 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1014))\)

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 available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
1014.3.c	\(\chi_{1014}(677, \cdot)\)	n/a	104	1
1014.3.d	\(\chi_{1014}(1013, \cdot)\)	n/a	104	1
1014.3.f	\(\chi_{1014}(577, \cdot)\)	1014.3.f.a	4	2
		1014.3.f.b	4
		1014.3.f.c	4
		1014.3.f.d	4
		1014.3.f.e	4
		1014.3.f.f	4
		1014.3.f.g	4
		1014.3.f.h	8
		1014.3.f.i	8
		1014.3.f.j	8
		1014.3.f.k	24
		1014.3.f.l	24
1014.3.h	\(\chi_{1014}(191, \cdot)\)	n/a	204	2
1014.3.j	\(\chi_{1014}(23, \cdot)\)	n/a	204	2
1014.3.l	\(\chi_{1014}(19, \cdot)\)	n/a	208	4
1014.3.n	\(\chi_{1014}(77, \cdot)\)	n/a	1440	12
1014.3.o	\(\chi_{1014}(53, \cdot)\)	n/a	1440	12
1014.3.s	\(\chi_{1014}(31, \cdot)\)	n/a	1488	24
1014.3.t	\(\chi_{1014}(17, \cdot)\)	n/a	2928	24
1014.3.v	\(\chi_{1014}(29, \cdot)\)	n/a	2928	24
1014.3.w	\(\chi_{1014}(7, \cdot)\)	n/a	2880	48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces

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