Space of modular forms of level 798 and weight 2

• Label: 798.2
• Level: 798
• Weight: 2
• Dimension: 4113
• Nonzero newspaces: 32
• Newform subspaces: 133
• Sturm bound: 69120
• Trace bound: 18

Defining parameters

Level:	\( N \)	=	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Newform subspaces:			\( 133 \)
Sturm bound:			\(69120\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(798))\).

	Total	New	Old
Modular forms	18144	4113	14031
Cusp forms	16417	4113	12304
Eisenstein series	1727	0	1727

Trace form

4113 * q - 3 * q^2 + q^3 + 5 * q^4 + 6 * q^5 + 9 * q^6 + 17 * q^7 - 3 * q^8 + 13 * q^9 + 6 * q^10 + 12 * q^11 + 13 * q^12 + 86 * q^13 + 21 * q^14 + 54 * q^15 - 3 * q^16 + 42 * q^17 - 27 * q^18 + 145 * q^19 + 54 * q^20 + 7 * q^21 + 72 * q^22 + 24 * q^23 - 15 * q^24 + 99 * q^25 + 54 * q^26 + 31 * q^27 + 21 * q^28 + 30 * q^29 + 6 * q^30 + 56 * q^31 - 3 * q^32 + 120 * q^33 - 6 * q^34 + 78 * q^35 + 13 * q^36 + 70 * q^37 - 3 * q^38 + 122 * q^39 + 6 * q^40 + 42 * q^41 + 45 * q^42 + 172 * q^43 + 12 * q^44 + 6 * q^45 + 24 * q^46 - 17 * q^48 + 33 * q^49 + 3 * q^50 - 240 * q^51 - 58 * q^52 - 90 * q^53 - 147 * q^54 - 144 * q^55 + 9 * q^56 - 191 * q^57 - 114 * q^58 - 84 * q^59 - 114 * q^60 - 82 * q^61 - 48 * q^62 - 113 * q^63 + 5 * q^64 - 12 * q^65 - 180 * q^66 - 12 * q^67 - 30 * q^68 - 132 * q^69 - 90 * q^70 + 3 * q^72 - 10 * q^73 - 42 * q^74 + 67 * q^75 - 23 * q^76 + 108 * q^77 + 78 * q^78 + 312 * q^79 + 6 * q^80 + 253 * q^81 + 162 * q^82 + 276 * q^83 + 91 * q^84 + 348 * q^85 + 132 * q^86 + 390 * q^87 - 12 * q^88 + 210 * q^89 + 186 * q^90 + 206 * q^91 + 120 * q^92 + 260 * q^93 + 288 * q^94 + 90 * q^95 - 15 * q^96 + 122 * q^97 + 93 * q^98 + 126 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(798))\)

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
798.2.a	\(\chi_{798}(1, \cdot)\)	798.2.a.a	1	1
		798.2.a.b	1
		798.2.a.c	1
		798.2.a.d	1
		798.2.a.e	1
		798.2.a.f	1
		798.2.a.g	1
		798.2.a.h	1
		798.2.a.i	1
		798.2.a.j	2
		798.2.a.k	2
		798.2.a.l	2
		798.2.a.m	2
798.2.b	\(\chi_{798}(113, \cdot)\)	798.2.b.a	2	1
		798.2.b.b	2
		798.2.b.c	2
		798.2.b.d	2
		798.2.b.e	8
		798.2.b.f	8
		798.2.b.g	8
		798.2.b.h	8
798.2.e	\(\chi_{798}(265, \cdot)\)	798.2.e.a	12	1
		798.2.e.b	12
798.2.f	\(\chi_{798}(419, \cdot)\)	798.2.f.a	24	1
		798.2.f.b	24
798.2.i	\(\chi_{798}(163, \cdot)\)	798.2.i.a	14	2
		798.2.i.b	14
		798.2.i.c	14
		798.2.i.d	14
798.2.j	\(\chi_{798}(457, \cdot)\)	798.2.j.a	2	2
		798.2.j.b	2
		798.2.j.c	2
		798.2.j.d	2
		798.2.j.e	2
		798.2.j.f	2
		798.2.j.g	4
		798.2.j.h	4
		798.2.j.i	6
		798.2.j.j	6
		798.2.j.k	8
		798.2.j.l	8
798.2.k	\(\chi_{798}(463, \cdot)\)	798.2.k.a	2	2
		798.2.k.b	2
		798.2.k.c	2
		798.2.k.d	2
		798.2.k.e	2
		798.2.k.f	2
		798.2.k.g	2
		798.2.k.h	2
		798.2.k.i	2
		798.2.k.j	4
		798.2.k.k	4
		798.2.k.l	4
		798.2.k.m	4
		798.2.k.n	6
798.2.l	\(\chi_{798}(121, \cdot)\)	798.2.l.a	14	2
		798.2.l.b	14
		798.2.l.c	14
		798.2.l.d	14
798.2.m	\(\chi_{798}(145, \cdot)\)	798.2.m.a	28	2
		798.2.m.b	28
798.2.p	\(\chi_{798}(107, \cdot)\)	798.2.p.a	2	2
		798.2.p.b	2
		798.2.p.c	50
		798.2.p.d	50
798.2.r	\(\chi_{798}(83, \cdot)\)	798.2.r.a	112	2
798.2.u	\(\chi_{798}(647, \cdot)\)	798.2.u.a	48	2
		798.2.u.b	48
798.2.w	\(\chi_{798}(311, \cdot)\)	798.2.w.a	104	2
798.2.ba	\(\chi_{798}(407, \cdot)\)	798.2.ba.a	2	2
		798.2.ba.b	2
		798.2.ba.c	2
		798.2.ba.d	2
		798.2.ba.e	2
		798.2.ba.f	2
		798.2.ba.g	4
		798.2.ba.h	4
		798.2.ba.i	4
		798.2.ba.j	4
		798.2.ba.k	12
		798.2.ba.l	12
		798.2.ba.m	14
		798.2.ba.n	14
798.2.bc	\(\chi_{798}(31, \cdot)\)	798.2.bc.a	28	2
		798.2.bc.b	28
798.2.be	\(\chi_{798}(493, \cdot)\)	798.2.be.a	28	2
		798.2.be.b	28
798.2.bf	\(\chi_{798}(569, \cdot)\)	798.2.bf.a	52	2
		798.2.bf.b	52
798.2.bh	\(\chi_{798}(65, \cdot)\)	798.2.bh.a	2	2
		798.2.bh.b	2
		798.2.bh.c	50
		798.2.bh.d	50
798.2.bj	\(\chi_{798}(559, \cdot)\)	798.2.bj.a	24	2
		798.2.bj.b	24
798.2.bn	\(\chi_{798}(353, \cdot)\)	798.2.bn.a	104	2
798.2.bo	\(\chi_{798}(43, \cdot)\)	798.2.bo.a	12	6
		798.2.bo.b	12
		798.2.bo.c	12
		798.2.bo.d	12
		798.2.bo.e	18
		798.2.bo.f	18
		798.2.bo.g	18
		798.2.bo.h	18
798.2.bp	\(\chi_{798}(289, \cdot)\)	798.2.bp.a	12	6
		798.2.bp.b	12
		798.2.bp.c	12
		798.2.bp.d	36
		798.2.bp.e	42
		798.2.bp.f	42
798.2.bq	\(\chi_{798}(25, \cdot)\)	798.2.bq.a	12	6
		798.2.bq.b	12
		798.2.bq.c	12
		798.2.bq.d	36
		798.2.bq.e	42
		798.2.bq.f	42
798.2.bt	\(\chi_{798}(5, \cdot)\)	798.2.bt.a	324	6
798.2.bu	\(\chi_{798}(53, \cdot)\)	798.2.bu.a	162	6
		798.2.bu.b	162
798.2.bx	\(\chi_{798}(13, \cdot)\)	798.2.bx.a	84	6
		798.2.bx.b	84
798.2.ca	\(\chi_{798}(325, \cdot)\)	798.2.ca.a	72	6
		798.2.ca.b	84
798.2.cb	\(\chi_{798}(17, \cdot)\)	798.2.cb.a	324	6
798.2.cc	\(\chi_{798}(317, \cdot)\)	798.2.cc.a	162	6
		798.2.cc.b	162
798.2.cf	\(\chi_{798}(29, \cdot)\)	798.2.cf.a	60	6
		798.2.cf.b	60
		798.2.cf.c	60
		798.2.cf.d	60
798.2.cg	\(\chi_{798}(251, \cdot)\)	798.2.cg.a	312	6
798.2.cj	\(\chi_{798}(241, \cdot)\)	798.2.cj.a	72	6
		798.2.cj.b	84

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(798))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(798)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 2}\)