Space of modular forms of level 3698 and weight 2

• Label: 3698.2
• Level: 3698
• Weight: 2
• Dimension: 142220
• Nonzero newspaces: 8
• Sturm bound: 1708476
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 3698 = 2 \cdot 43^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(1708476\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3698))\).

	Total	New	Old
Modular forms	429807	142220	287587
Cusp forms	424432	142220	282212
Eisenstein series	5375	0	5375

Trace form

142220 * q + q^2 + 4 * q^3 + q^4 + 6 * q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + 6 * q^10 + 12 * q^11 + 4 * q^12 + 14 * q^13 + 8 * q^14 + 24 * q^15 + q^16 + 18 * q^17 + 13 * q^18 + 20 * q^19 + 6 * q^20 + 32 * q^21 + 12 * q^22 + 24 * q^23 + 4 * q^24 + 31 * q^25 + 14 * q^26 + 40 * q^27 + 8 * q^28 + 30 * q^29 + 24 * q^30 + 4 * q^31 + q^32 - 120 * q^33 - 108 * q^34 - 120 * q^35 - 99 * q^36 - 130 * q^37 - 148 * q^38 - 140 * q^39 + 6 * q^40 - 42 * q^41 - 136 * q^42 - 210 * q^43 - 72 * q^44 - 342 * q^45 - 144 * q^46 - 36 * q^47 + 4 * q^48 - 139 * q^49 - 137 * q^50 - 96 * q^51 - 98 * q^52 - 114 * q^53 - 86 * q^54 - 96 * q^55 + 8 * q^56 + 52 * q^57 + 30 * q^58 + 60 * q^59 + 24 * q^60 + 62 * q^61 + 32 * q^62 + 104 * q^63 + q^64 + 84 * q^65 + 48 * q^66 + 68 * q^67 + 18 * q^68 + 12 * q^69 + 48 * q^70 - 12 * q^71 + 13 * q^72 - 10 * q^73 + 38 * q^74 - 170 * q^75 + 20 * q^76 - 156 * q^77 + 56 * q^78 - 88 * q^79 + 6 * q^80 - 215 * q^81 + 42 * q^82 - 84 * q^83 + 32 * q^84 - 60 * q^85 - 300 * q^87 + 12 * q^88 - 78 * q^89 + 78 * q^90 - 56 * q^91 + 24 * q^92 - 208 * q^93 + 48 * q^94 - 48 * q^95 + 4 * q^96 - 154 * q^97 + 57 * q^98 - 138 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3698))\)

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
3698.2.a	\(\chi_{3698}(1, \cdot)\)	3698.2.a.a	1	1
		3698.2.a.b	1
		3698.2.a.c	2
		3698.2.a.d	2
		3698.2.a.e	2
		3698.2.a.f	2
		3698.2.a.g	2
		3698.2.a.h	2
		3698.2.a.i	5
		3698.2.a.j	5
		3698.2.a.k	6
		3698.2.a.l	6
		3698.2.a.m	6
		3698.2.a.n	6
		3698.2.a.o	9
		3698.2.a.p	9
		3698.2.a.q	10
		3698.2.a.r	10
		3698.2.a.s	12
		3698.2.a.t	12
		3698.2.a.u	20
		3698.2.a.v	20
3698.2.c	\(\chi_{3698}(423, \cdot)\)	n/a	302	2
3698.2.e	\(\chi_{3698}(403, \cdot)\)	n/a	894	6
3698.2.g	\(\chi_{3698}(361, \cdot)\)	n/a	1812	12
3698.2.i	\(\chi_{3698}(87, \cdot)\)	n/a	6678	42
3698.2.k	\(\chi_{3698}(49, \cdot)\)	n/a	13188	84
3698.2.m	\(\chi_{3698}(11, \cdot)\)	n/a	40068	252
3698.2.o	\(\chi_{3698}(9, \cdot)\)	n/a	79128	504

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3698))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3698)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1849))\)\(^{\oplus 2}\)