Space of modular forms of level 35 and weight 3

• Label: 35.3
• Level: 35
• Weight: 3
• Dimension: 70
• Nonzero newspaces: 6
• Newform subspaces: 9
• Sturm bound: 288
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(35))\).

	Total	New	Old
Modular forms	120	98	22
Cusp forms	72	70	2
Eisenstein series	48	28	20

Trace form

70 * q - 6 * q^2 - 12 * q^3 - 22 * q^4 - 12 * q^5 - 24 * q^6 + 2 * q^7 - 18 * q^8 - 30 * q^9 - 12 * q^10 - 12 * q^11 - 12 * q^12 - 12 * q^13 - 54 * q^14 - 24 * q^15 - 2 * q^16 - 12 * q^17 + 42 * q^18 - 12 * q^19 - 12 * q^20 - 24 * q^21 - 60 * q^22 - 48 * q^23 + 180 * q^24 + 46 * q^25 + 168 * q^26 + 240 * q^27 + 346 * q^28 + 204 * q^29 + 276 * q^30 + 48 * q^31 + 42 * q^32 + 48 * q^33 - 48 * q^35 - 330 * q^36 - 44 * q^37 - 204 * q^38 - 312 * q^39 - 444 * q^40 - 192 * q^41 - 588 * q^42 - 356 * q^43 - 432 * q^44 - 408 * q^45 - 204 * q^46 - 168 * q^47 - 444 * q^48 - 110 * q^49 + 126 * q^50 - 24 * q^51 + 180 * q^52 + 420 * q^54 + 324 * q^55 + 558 * q^56 + 552 * q^57 + 720 * q^58 + 468 * q^59 + 1068 * q^60 + 552 * q^61 + 744 * q^62 + 690 * q^63 + 878 * q^64 + 276 * q^65 + 408 * q^66 + 416 * q^67 + 168 * q^68 - 192 * q^70 - 372 * q^71 - 546 * q^72 - 396 * q^73 - 900 * q^74 - 588 * q^75 - 1032 * q^76 - 672 * q^77 - 1320 * q^78 - 784 * q^79 - 1008 * q^80 - 1050 * q^81 - 1572 * q^82 - 684 * q^83 - 1020 * q^84 - 792 * q^85 - 60 * q^86 + 168 * q^87 + 336 * q^88 + 888 * q^89 + 900 * q^90 + 600 * q^91 + 1524 * q^92 + 912 * q^93 + 948 * q^94 + 852 * q^95 + 1320 * q^96 + 492 * q^97 + 1146 * q^98 + 564 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.3.c	\(\chi_{35}(34, \cdot)\)	35.3.c.a	1	1
		35.3.c.b	1
		35.3.c.c	4
35.3.d	\(\chi_{35}(6, \cdot)\)	35.3.d.a	2	1
		35.3.d.b	2
35.3.g	\(\chi_{35}(8, \cdot)\)	35.3.g.a	12	2
35.3.h	\(\chi_{35}(26, \cdot)\)	35.3.h.a	12	2
35.3.i	\(\chi_{35}(19, \cdot)\)	35.3.i.a	12	2
35.3.l	\(\chi_{35}(2, \cdot)\)	35.3.l.a	24	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)