Space of modular forms of level 1035 and weight 4

• Label: 1035.4
• Level: 1035
• Weight: 4
• Dimension: 81884
• Nonzero newspaces: 24
• Sturm bound: 304128
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(304128\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1035))\).

	Total	New	Old
Modular forms	115456	83020	32436
Cusp forms	112640	81884	30756
Eisenstein series	2816	1136	1680

Trace form

81884 * q - 62 * q^2 - 84 * q^3 - 126 * q^4 - 111 * q^5 - 196 * q^6 - 18 * q^7 + 78 * q^8 - 20 * q^9 - 473 * q^10 - 446 * q^11 - 440 * q^12 + 166 * q^13 + 630 * q^14 + 274 * q^15 + 1878 * q^16 + 1242 * q^17 + 792 * q^18 - 1170 * q^19 - 2739 * q^20 - 1284 * q^21 - 3688 * q^22 - 1898 * q^23 - 1124 * q^24 + 325 * q^25 - 862 * q^26 - 696 * q^27 + 4458 * q^28 + 3454 * q^29 + 2780 * q^30 + 3922 * q^31 + 8178 * q^32 + 2944 * q^33 + 2886 * q^34 + 2419 * q^35 + 724 * q^36 - 586 * q^37 - 844 * q^38 - 108 * q^39 - 5971 * q^40 - 6174 * q^41 - 8824 * q^42 - 5462 * q^43 - 15128 * q^44 - 5986 * q^45 - 9802 * q^46 - 12204 * q^47 - 9644 * q^48 - 5648 * q^49 - 4689 * q^50 - 4 * q^51 + 5114 * q^52 + 4694 * q^53 - 276 * q^54 - 1157 * q^55 - 15440 * q^56 - 2940 * q^57 + 9512 * q^58 + 5954 * q^59 + 5116 * q^60 + 3378 * q^61 + 15006 * q^62 + 12892 * q^63 + 20194 * q^64 + 16423 * q^65 + 19728 * q^66 + 2466 * q^67 + 54368 * q^68 + 16654 * q^69 + 13110 * q^70 + 30974 * q^71 + 41108 * q^72 - 1082 * q^73 + 26968 * q^74 + 12222 * q^75 + 29444 * q^76 + 16874 * q^77 + 2272 * q^78 + 1898 * q^79 - 10456 * q^80 - 17604 * q^81 - 10226 * q^82 - 37198 * q^83 - 64624 * q^84 - 14449 * q^85 - 71454 * q^86 - 22308 * q^87 - 36222 * q^88 - 44442 * q^89 - 43612 * q^90 - 40012 * q^91 - 34944 * q^92 - 19724 * q^93 - 18952 * q^94 - 19485 * q^95 - 12136 * q^96 - 21514 * q^97 - 24722 * q^98 + 180 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1035))\)

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
1035.4.a	\(\chi_{1035}(1, \cdot)\)	1035.4.a.a	1	1
		1035.4.a.b	1
		1035.4.a.c	1
		1035.4.a.d	1
		1035.4.a.e	1
		1035.4.a.f	1
		1035.4.a.g	2
		1035.4.a.h	3
		1035.4.a.i	4
		1035.4.a.j	4
		1035.4.a.k	5
		1035.4.a.l	5
		1035.4.a.m	5
		1035.4.a.n	6
		1035.4.a.o	6
		1035.4.a.p	6
		1035.4.a.q	6
		1035.4.a.r	8
		1035.4.a.s	9
		1035.4.a.t	9
		1035.4.a.u	13
		1035.4.a.v	13
1035.4.b	\(\chi_{1035}(829, \cdot)\)	n/a	166	1
1035.4.c	\(\chi_{1035}(206, \cdot)\)	1035.4.c.a	48	1
		1035.4.c.b	48
1035.4.h	\(\chi_{1035}(1034, \cdot)\)	n/a	144	1
1035.4.i	\(\chi_{1035}(346, \cdot)\)	n/a	528	2
1035.4.j	\(\chi_{1035}(323, \cdot)\)	n/a	264	2
1035.4.k	\(\chi_{1035}(298, \cdot)\)	n/a	356	2
1035.4.n	\(\chi_{1035}(344, \cdot)\)	n/a	856	2
1035.4.s	\(\chi_{1035}(551, \cdot)\)	n/a	576	2
1035.4.t	\(\chi_{1035}(139, \cdot)\)	n/a	792	2
1035.4.u	\(\chi_{1035}(271, \cdot)\)	n/a	1200	10
1035.4.x	\(\chi_{1035}(47, \cdot)\)	n/a	1584	4
1035.4.y	\(\chi_{1035}(22, \cdot)\)	n/a	1712	4
1035.4.z	\(\chi_{1035}(44, \cdot)\)	n/a	1440	10
1035.4.be	\(\chi_{1035}(251, \cdot)\)	n/a	960	10
1035.4.bf	\(\chi_{1035}(64, \cdot)\)	n/a	1780	10
1035.4.bg	\(\chi_{1035}(16, \cdot)\)	n/a	5760	20
1035.4.bj	\(\chi_{1035}(28, \cdot)\)	n/a	3560	20
1035.4.bk	\(\chi_{1035}(8, \cdot)\)	n/a	2880	20
1035.4.bl	\(\chi_{1035}(4, \cdot)\)	n/a	8560	20
1035.4.bm	\(\chi_{1035}(11, \cdot)\)	n/a	5760	20
1035.4.br	\(\chi_{1035}(14, \cdot)\)	n/a	8560	20
1035.4.bs	\(\chi_{1035}(7, \cdot)\)	n/a	17120	40
1035.4.bt	\(\chi_{1035}(2, \cdot)\)	n/a	17120	40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1035))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1035)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 2}\)