Space of modular forms of level 1014 and weight 4

• Label: 1014.4
• Level: 1014
• Weight: 4
• Dimension: 21043
• Nonzero newspaces: 12
• Sturm bound: 227136
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(227136\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1014))\).

	Total	New	Old
Modular forms	86088	21043	65045
Cusp forms	84264	21043	63221
Eisenstein series	1824	0	1824

Trace form

21043 * q - 2 * q^2 - 3 * q^3 + 4 * q^4 + 6 * q^5 + 6 * q^6 + 272 * q^7 + 88 * q^8 + 9 * q^9 - 372 * q^10 - 468 * q^11 - 108 * q^12 - 576 * q^13 - 448 * q^14 - 306 * q^15 + 16 * q^16 + 822 * q^17 + 198 * q^18 + 2756 * q^19 + 552 * q^20 + 288 * q^21 - 24 * q^22 - 744 * q^23 + 24 * q^24 - 1589 * q^25 - 1683 * q^27 - 64 * q^28 - 750 * q^29 - 1596 * q^30 + 152 * q^31 - 32 * q^32 + 2028 * q^33 + 252 * q^34 + 3024 * q^35 + 1572 * q^36 + 1538 * q^37 - 40 * q^38 + 2244 * q^39 - 48 * q^40 + 750 * q^41 + 1776 * q^42 + 1292 * q^43 + 48 * q^44 - 534 * q^45 - 336 * q^46 - 1584 * q^47 - 48 * q^48 - 807 * q^49 + 1930 * q^50 - 2070 * q^51 + 552 * q^52 + 4374 * q^53 + 3366 * q^54 + 72 * q^55 + 512 * q^56 - 1188 * q^57 - 2436 * q^58 - 5316 * q^59 - 2184 * q^60 - 3190 * q^61 - 8176 * q^62 - 16296 * q^63 - 704 * q^64 - 5358 * q^65 - 5880 * q^66 - 7228 * q^67 - 1128 * q^68 - 7536 * q^69 - 4704 * q^70 - 1320 * q^71 - 456 * q^72 + 4826 * q^73 + 11036 * q^74 + 22707 * q^75 + 11024 * q^76 + 26304 * q^77 + 5832 * q^78 + 21560 * q^79 + 2208 * q^80 + 16305 * q^81 - 636 * q^82 - 5388 * q^83 - 2496 * q^84 - 15168 * q^85 - 6616 * q^86 - 12570 * q^87 - 96 * q^88 - 10950 * q^89 - 4428 * q^90 - 9360 * q^91 - 7776 * q^92 - 19872 * q^93 - 18528 * q^94 - 13320 * q^95 + 96 * q^96 - 28270 * q^97 - 3090 * q^98 - 13572 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1014))\)

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
1014.4.a	\(\chi_{1014}(1, \cdot)\)	1014.4.a.a	1	1
		1014.4.a.b	1
		1014.4.a.c	1
		1014.4.a.d	1
		1014.4.a.e	1
		1014.4.a.f	1
		1014.4.a.g	1
		1014.4.a.h	1
		1014.4.a.i	1
		1014.4.a.j	1
		1014.4.a.k	1
		1014.4.a.l	2
		1014.4.a.m	2
		1014.4.a.n	2
		1014.4.a.o	2
		1014.4.a.p	2
		1014.4.a.q	2
		1014.4.a.r	2
		1014.4.a.s	2
		1014.4.a.t	3
		1014.4.a.u	3
		1014.4.a.v	3
		1014.4.a.w	3
		1014.4.a.x	3
		1014.4.a.y	3
		1014.4.a.z	4
		1014.4.a.ba	4
		1014.4.a.bb	6
		1014.4.a.bc	6
		1014.4.a.bd	6
		1014.4.a.be	6
1014.4.b	\(\chi_{1014}(337, \cdot)\)	1014.4.b.a	2	1
		1014.4.b.b	2
		1014.4.b.c	2
		1014.4.b.d	2
		1014.4.b.e	2
		1014.4.b.f	2
		1014.4.b.g	2
		1014.4.b.h	2
		1014.4.b.i	4
		1014.4.b.j	4
		1014.4.b.k	4
		1014.4.b.l	6
		1014.4.b.m	6
		1014.4.b.n	6
		1014.4.b.o	8
		1014.4.b.p	12
		1014.4.b.q	12
1014.4.e	\(\chi_{1014}(529, \cdot)\)	n/a	152	2
1014.4.g	\(\chi_{1014}(239, \cdot)\)	n/a	308	2
1014.4.i	\(\chi_{1014}(361, \cdot)\)	n/a	156	2
1014.4.k	\(\chi_{1014}(89, \cdot)\)	n/a	616	4
1014.4.m	\(\chi_{1014}(79, \cdot)\)	n/a	1104	12
1014.4.p	\(\chi_{1014}(25, \cdot)\)	n/a	1080	12
1014.4.q	\(\chi_{1014}(55, \cdot)\)	n/a	2208	24
1014.4.r	\(\chi_{1014}(5, \cdot)\)	n/a	4368	24
1014.4.u	\(\chi_{1014}(43, \cdot)\)	n/a	2160	24
1014.4.x	\(\chi_{1014}(11, \cdot)\)	n/a	8736	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces

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