Space of modular forms of level 35 and weight 5

• Label: 35.5
• Level: 35
• Weight: 5
• Dimension: 154
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 480
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(35))\).

	Total	New	Old
Modular forms	216	182	34
Cusp forms	168	154	14
Eisenstein series	48	28	20

Trace form

154 * q - 2 * q^2 + 58 * q^4 - 62 * q^5 - 72 * q^6 - 58 * q^7 - 450 * q^8 - 126 * q^9 + 212 * q^10 + 536 * q^11 + 828 * q^12 - 568 * q^13 - 1230 * q^14 + 348 * q^15 + 358 * q^16 + 484 * q^17 - 642 * q^18 - 1296 * q^19 - 852 * q^20 + 1452 * q^21 + 2884 * q^22 + 1540 * q^23 + 1620 * q^24 + 3208 * q^25 + 1376 * q^26 + 888 * q^27 - 3518 * q^28 - 2100 * q^29 - 13572 * q^30 - 13364 * q^31 - 15806 * q^32 - 8244 * q^33 + 5210 * q^35 + 18198 * q^36 + 11140 * q^37 + 23124 * q^38 + 18744 * q^39 + 24948 * q^40 + 12272 * q^41 + 36 * q^42 - 9116 * q^43 - 16776 * q^44 - 13692 * q^45 - 19628 * q^46 - 18524 * q^47 - 19500 * q^48 - 2854 * q^49 - 15542 * q^50 + 9396 * q^51 + 17228 * q^52 + 33496 * q^53 + 37572 * q^54 + 29524 * q^55 + 37926 * q^56 - 528 * q^57 + 6528 * q^58 - 13704 * q^59 - 43056 * q^60 - 39236 * q^61 - 54424 * q^62 - 59586 * q^63 - 57962 * q^64 - 58100 * q^65 - 47664 * q^66 - 35724 * q^67 - 58408 * q^68 + 23208 * q^70 + 52460 * q^71 + 81390 * q^72 + 42644 * q^73 + 75684 * q^74 + 97638 * q^75 + 93720 * q^76 + 89380 * q^77 + 108648 * q^78 + 79180 * q^79 + 65656 * q^80 - 39210 * q^81 - 6500 * q^82 - 42788 * q^83 - 67716 * q^84 - 50560 * q^85 - 43228 * q^86 - 17904 * q^87 + 35088 * q^88 - 25692 * q^89 + 4680 * q^90 - 28960 * q^91 - 59996 * q^92 - 61236 * q^93 - 140028 * q^94 - 89946 * q^95 - 141144 * q^96 - 46888 * q^97 - 60498 * q^98 - 70428 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.5.c	\(\chi_{35}(34, \cdot)\)	35.5.c.a	1	1
		35.5.c.b	1
		35.5.c.c	2
		35.5.c.d	2
		35.5.c.e	8
35.5.d	\(\chi_{35}(6, \cdot)\)	35.5.d.a	12	1
35.5.g	\(\chi_{35}(8, \cdot)\)	35.5.g.a	24	2
35.5.h	\(\chi_{35}(26, \cdot)\)	35.5.h.a	20	2
35.5.i	\(\chi_{35}(19, \cdot)\)	35.5.i.a	28	2
35.5.l	\(\chi_{35}(2, \cdot)\)	35.5.l.a	56	4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

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