Space of modular forms of level 1014 and weight 6

• Label: 1014.6
• Level: 1014
• Weight: 6
• Dimension: 35071
• Nonzero newspaces: 12
• Sturm bound: 340704
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(340704\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1014))\).

	Total	New	Old
Modular forms	142872	35071	107801
Cusp forms	141048	35071	105977
Eisenstein series	1824	0	1824

Trace form

35071 * q + 4 * q^2 - 9 * q^3 + 16 * q^4 - 66 * q^5 - 36 * q^6 + 2560 * q^7 - 704 * q^8 - 567 * q^9 - 504 * q^10 + 4212 * q^11 + 1008 * q^12 + 6288 * q^13 + 2816 * q^14 - 4158 * q^15 - 3840 * q^16 - 4290 * q^17 - 3564 * q^18 - 19988 * q^19 + 6816 * q^20 - 1320 * q^21 - 240 * q^22 + 13512 * q^23 - 576 * q^24 + 38731 * q^25 + 29583 * q^27 + 2816 * q^28 - 12126 * q^29 + 39048 * q^30 - 55960 * q^31 + 1024 * q^32 + 84 * q^33 - 1656 * q^34 + 23184 * q^35 - 40944 * q^36 + 64994 * q^37 + 3824 * q^38 - 45804 * q^39 - 4224 * q^40 + 11766 * q^41 - 6624 * q^42 - 134588 * q^43 - 960 * q^44 + 238866 * q^45 + 2400 * q^46 - 9648 * q^47 - 2304 * q^48 + 43433 * q^49 + 143116 * q^50 + 128574 * q^51 + 5856 * q^52 - 97938 * q^53 - 239364 * q^54 - 478680 * q^55 - 157696 * q^56 - 348972 * q^57 - 150936 * q^58 - 199644 * q^59 + 56352 * q^60 - 98950 * q^61 + 434336 * q^62 + 373008 * q^63 + 53248 * q^64 + 413502 * q^65 + 345840 * q^66 + 810412 * q^67 + 12768 * q^68 + 346200 * q^69 - 242880 * q^70 - 281400 * q^71 - 212928 * q^72 - 458870 * q^73 - 79384 * q^74 - 1100079 * q^75 - 319808 * q^76 - 1320672 * q^77 - 214128 * q^78 - 1082296 * q^79 + 109056 * q^80 + 625929 * q^81 - 484680 * q^82 - 425652 * q^83 - 65664 * q^84 + 807096 * q^85 + 391568 * q^86 + 1532154 * q^87 - 3840 * q^88 + 1149258 * q^89 + 367416 * q^90 + 832936 * q^91 + 717696 * q^92 + 36264 * q^93 + 1020480 * q^94 + 421704 * q^95 - 9216 * q^96 - 2192830 * q^97 - 434460 * q^98 - 544068 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1014))\)

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
1014.6.a	\(\chi_{1014}(1, \cdot)\)	1014.6.a.a	1	1
		1014.6.a.b	1
		1014.6.a.c	1
		1014.6.a.d	1
		1014.6.a.e	1
		1014.6.a.f	1
		1014.6.a.g	1
		1014.6.a.h	2
		1014.6.a.i	2
		1014.6.a.j	2
		1014.6.a.k	2
		1014.6.a.l	2
		1014.6.a.m	2
		1014.6.a.n	3
		1014.6.a.o	3
		1014.6.a.p	3
		1014.6.a.q	3
		1014.6.a.r	3
		1014.6.a.s	3
		1014.6.a.t	4
		1014.6.a.u	4
		1014.6.a.v	6
		1014.6.a.w	6
		1014.6.a.x	6
		1014.6.a.y	6
		1014.6.a.z	6
		1014.6.a.ba	6
		1014.6.a.bb	6
		1014.6.a.bc	6
		1014.6.a.bd	9
		1014.6.a.be	9
		1014.6.a.bf	9
		1014.6.a.bg	9
1014.6.b	\(\chi_{1014}(337, \cdot)\)	n/a	126	1
1014.6.e	\(\chi_{1014}(529, \cdot)\)	n/a	260	2
1014.6.g	\(\chi_{1014}(239, \cdot)\)	n/a	516	2
1014.6.i	\(\chi_{1014}(361, \cdot)\)	n/a	256	2
1014.6.k	\(\chi_{1014}(89, \cdot)\)	n/a	1024	4
1014.6.m	\(\chi_{1014}(79, \cdot)\)	n/a	1824	12
1014.6.p	\(\chi_{1014}(25, \cdot)\)	n/a	1848	12
1014.6.q	\(\chi_{1014}(55, \cdot)\)	n/a	3600	24
1014.6.r	\(\chi_{1014}(5, \cdot)\)	n/a	7248	24
1014.6.u	\(\chi_{1014}(43, \cdot)\)	n/a	3648	24
1014.6.x	\(\chi_{1014}(11, \cdot)\)	n/a	14592	48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces

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