Space of modular forms of level 35 and weight 4

• Label: 35.4
• Level: 35
• Weight: 4
• Dimension: 112
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 384
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(384\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(35))\).

	Total	New	Old
Modular forms	168	144	24
Cusp forms	120	112	8
Eisenstein series	48	32	16

Trace form

112 * q + 2 * q^2 + 2 * q^3 - 22 * q^4 - 11 * q^5 - 68 * q^6 - 60 * q^7 + 42 * q^8 + 124 * q^9 - 22 * q^10 - 82 * q^11 - 128 * q^12 + 64 * q^13 - 30 * q^14 - 70 * q^15 - 10 * q^16 - 214 * q^17 - 154 * q^18 + 106 * q^19 + 236 * q^20 + 426 * q^21 + 256 * q^22 - 270 * q^23 - 1056 * q^24 - 941 * q^25 - 1240 * q^26 - 664 * q^27 - 822 * q^28 + 160 * q^29 + 982 * q^30 + 990 * q^31 + 2134 * q^32 + 1678 * q^33 + 2092 * q^34 + 1305 * q^35 + 3422 * q^36 + 1394 * q^37 + 1820 * q^38 + 896 * q^39 - 132 * q^40 - 2024 * q^41 - 2304 * q^42 - 1580 * q^43 - 3284 * q^44 - 2456 * q^45 - 3540 * q^46 - 46 * q^47 - 1736 * q^48 + 344 * q^49 + 986 * q^50 - 206 * q^51 + 332 * q^52 + 914 * q^53 - 3344 * q^54 - 2878 * q^55 - 3894 * q^56 - 6412 * q^57 - 6448 * q^58 - 4810 * q^59 - 2792 * q^60 + 946 * q^61 - 624 * q^62 + 2088 * q^63 + 5158 * q^64 + 2590 * q^65 + 8588 * q^66 + 6126 * q^67 + 9244 * q^68 + 11556 * q^69 + 12666 * q^70 + 5608 * q^71 + 10866 * q^72 + 6394 * q^73 + 8968 * q^74 + 2237 * q^75 + 1508 * q^76 + 270 * q^77 - 392 * q^78 - 4314 * q^79 - 6616 * q^80 - 7922 * q^81 - 8512 * q^82 - 7764 * q^83 - 15648 * q^84 - 8542 * q^85 - 12184 * q^86 - 12400 * q^87 - 17772 * q^88 - 9990 * q^89 - 12844 * q^90 - 2364 * q^91 - 8136 * q^92 + 174 * q^93 - 1952 * q^94 + 4435 * q^95 + 5924 * q^96 + 5612 * q^97 + 4258 * q^98 + 8624 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.4.a	\(\chi_{35}(1, \cdot)\)	35.4.a.a	1	1
		35.4.a.b	2
		35.4.a.c	3
35.4.b	\(\chi_{35}(29, \cdot)\)	35.4.b.a	10	1
35.4.e	\(\chi_{35}(11, \cdot)\)	35.4.e.a	2	2
		35.4.e.b	4
		35.4.e.c	10
35.4.f	\(\chi_{35}(13, \cdot)\)	35.4.f.a	4	2
		35.4.f.b	16
35.4.j	\(\chi_{35}(4, \cdot)\)	35.4.j.a	20	2
35.4.k	\(\chi_{35}(3, \cdot)\)	35.4.k.a	40	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)