Space of modular forms of level 882 and weight 2

• Label: 882.2
• Level: 882
• Weight: 2
• Dimension: 5360
• Nonzero newspaces: 20
• Newform subspaces: 129
• Sturm bound: 84672
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 129 \)
Sturm bound:			\(84672\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(882))\).

	Total	New	Old
Modular forms	22128	5360	16768
Cusp forms	20209	5360	14849
Eisenstein series	1919	0	1919

Trace form

5360 * q - q^2 - 3 * q^3 - 5 * q^4 - 12 * q^5 + 3 * q^6 - 8 * q^7 + 2 * q^8 + 3 * q^9 - 12 * q^10 - 21 * q^11 - 6 * q^13 + 18 * q^14 + 48 * q^15 + 11 * q^16 + 90 * q^17 + 42 * q^18 + 66 * q^19 + 36 * q^20 + 36 * q^21 + 75 * q^22 + 102 * q^23 + 21 * q^24 + 65 * q^25 + 64 * q^26 + 72 * q^27 + 42 * q^29 + 24 * q^30 + 12 * q^31 - q^32 + 39 * q^33 - 21 * q^34 + 30 * q^35 + 3 * q^36 + 64 * q^37 + 7 * q^38 + 72 * q^39 + 30 * q^40 + 171 * q^41 + 77 * q^43 + 12 * q^44 + 96 * q^45 + 66 * q^46 + 162 * q^47 + 3 * q^48 + 186 * q^49 - 31 * q^50 - 63 * q^51 + 32 * q^52 - 36 * q^53 - 135 * q^54 + 210 * q^55 + 36 * q^56 - 189 * q^57 + 126 * q^58 - 147 * q^59 - 144 * q^60 + 134 * q^61 - 134 * q^62 - 168 * q^63 - 2 * q^64 - 336 * q^65 - 192 * q^66 + 67 * q^67 - 117 * q^68 - 216 * q^69 + 18 * q^70 - 168 * q^71 + 3 * q^72 - 18 * q^73 - 140 * q^74 - 183 * q^75 - 3 * q^76 - 72 * q^77 - 102 * q^78 - 20 * q^79 - 12 * q^80 + 15 * q^81 - 54 * q^82 + 60 * q^83 - 36 * q^85 - 23 * q^86 + 162 * q^87 + 27 * q^88 + 216 * q^89 + 96 * q^90 + 142 * q^91 + 54 * q^92 + 216 * q^93 + 78 * q^94 + 456 * q^95 + 24 * q^96 + 207 * q^97 + 96 * q^98 + 258 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)

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
882.2.a	\(\chi_{882}(1, \cdot)\)	882.2.a.a	1	1
		882.2.a.b	1
		882.2.a.c	1
		882.2.a.d	1
		882.2.a.e	1
		882.2.a.f	1
		882.2.a.g	1
		882.2.a.h	1
		882.2.a.i	1
		882.2.a.j	1
		882.2.a.k	1
		882.2.a.l	1
		882.2.a.m	2
		882.2.a.n	2
		882.2.a.o	2
882.2.d	\(\chi_{882}(881, \cdot)\)	882.2.d.a	8	1
		882.2.d.b	8
882.2.e	\(\chi_{882}(373, \cdot)\)	882.2.e.a	2	2
		882.2.e.b	2
		882.2.e.c	2
		882.2.e.d	2
		882.2.e.e	2
		882.2.e.f	2
		882.2.e.g	2
		882.2.e.h	2
		882.2.e.i	2
		882.2.e.j	2
		882.2.e.k	4
		882.2.e.l	4
		882.2.e.m	4
		882.2.e.n	4
		882.2.e.o	6
		882.2.e.p	6
		882.2.e.q	8
		882.2.e.r	8
		882.2.e.s	8
		882.2.e.t	8
882.2.f	\(\chi_{882}(295, \cdot)\)	882.2.f.a	2	2
		882.2.f.b	2
		882.2.f.c	2
		882.2.f.d	2
		882.2.f.e	2
		882.2.f.f	2
		882.2.f.g	2
		882.2.f.h	2
		882.2.f.i	2
		882.2.f.j	4
		882.2.f.k	4
		882.2.f.l	6
		882.2.f.m	6
		882.2.f.n	6
		882.2.f.o	6
		882.2.f.p	8
		882.2.f.q	8
		882.2.f.r	8
		882.2.f.s	8
882.2.g	\(\chi_{882}(361, \cdot)\)	882.2.g.a	2	2
		882.2.g.b	2
		882.2.g.c	2
		882.2.g.d	2
		882.2.g.e	2
		882.2.g.f	2
		882.2.g.g	2
		882.2.g.h	2
		882.2.g.i	2
		882.2.g.j	2
		882.2.g.k	4
		882.2.g.l	4
		882.2.g.m	4
882.2.h	\(\chi_{882}(67, \cdot)\)	882.2.h.a	2	2
		882.2.h.b	2
		882.2.h.c	2
		882.2.h.d	2
		882.2.h.e	2
		882.2.h.f	2
		882.2.h.g	2
		882.2.h.h	2
		882.2.h.i	2
		882.2.h.j	2
		882.2.h.k	4
		882.2.h.l	4
		882.2.h.m	4
		882.2.h.n	4
		882.2.h.o	6
		882.2.h.p	6
		882.2.h.q	8
		882.2.h.r	8
		882.2.h.s	8
		882.2.h.t	8
882.2.k	\(\chi_{882}(215, \cdot)\)	882.2.k.a	8	2
		882.2.k.b	16
882.2.l	\(\chi_{882}(227, \cdot)\)	882.2.l.a	16	2
		882.2.l.b	16
		882.2.l.c	48
882.2.m	\(\chi_{882}(293, \cdot)\)	882.2.m.a	16	2
		882.2.m.b	16
		882.2.m.c	48
882.2.t	\(\chi_{882}(803, \cdot)\)	882.2.t.a	16	2
		882.2.t.b	16
		882.2.t.c	48
882.2.u	\(\chi_{882}(127, \cdot)\)	882.2.u.a	6	6
		882.2.u.b	6
		882.2.u.c	6
		882.2.u.d	12
		882.2.u.e	12
		882.2.u.f	18
		882.2.u.g	18
		882.2.u.h	18
		882.2.u.i	18
		882.2.u.j	18
882.2.v	\(\chi_{882}(125, \cdot)\)	882.2.v.a	96	6
882.2.y	\(\chi_{882}(193, \cdot)\)	882.2.y.a	336	12
		882.2.y.b	336
882.2.z	\(\chi_{882}(37, \cdot)\)	882.2.z.a	24	12
		882.2.z.b	24
		882.2.z.c	24
		882.2.z.d	24
		882.2.z.e	36
		882.2.z.f	36
		882.2.z.g	60
		882.2.z.h	60
882.2.ba	\(\chi_{882}(43, \cdot)\)	882.2.ba.a	336	12
		882.2.ba.b	336
882.2.bb	\(\chi_{882}(25, \cdot)\)	882.2.bb.a	336	12
		882.2.bb.b	336
882.2.bc	\(\chi_{882}(47, \cdot)\)	882.2.bc.a	672	12
882.2.bj	\(\chi_{882}(41, \cdot)\)	882.2.bj.a	672	12
882.2.bk	\(\chi_{882}(5, \cdot)\)	882.2.bk.a	672	12
882.2.bl	\(\chi_{882}(17, \cdot)\)	882.2.bl.a	240	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(882))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(882)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)