Space of modular forms of level 882 and weight 3

• Label: 882.3
• Level: 882
• Weight: 3
• Dimension: 10722
• Nonzero newspaces: 20
• Sturm bound: 127008
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(127008\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(882))\).

	Total	New	Old
Modular forms	43296	10722	32574
Cusp forms	41376	10722	30654
Eisenstein series	1920	0	1920

Trace form

10722 * q + 8 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^7 + 12 * q^9 - 36 * q^10 - 18 * q^11 + 12 * q^12 - 106 * q^13 - 108 * q^14 - 222 * q^15 - 48 * q^16 - 372 * q^17 - 120 * q^18 - 196 * q^19 - 36 * q^20 + 36 * q^21 + 84 * q^22 + 390 * q^23 + 96 * q^24 + 570 * q^25 + 528 * q^26 + 504 * q^27 + 84 * q^28 + 786 * q^29 + 312 * q^30 - 94 * q^31 - 330 * q^33 + 60 * q^34 - 390 * q^35 + 12 * q^36 - 816 * q^37 - 468 * q^38 - 246 * q^39 - 264 * q^40 - 714 * q^41 - 338 * q^43 - 240 * q^44 + 330 * q^45 - 300 * q^46 + 486 * q^47 + 24 * q^48 + 312 * q^49 + 936 * q^50 + 2232 * q^51 - 212 * q^52 + 2808 * q^53 + 1188 * q^54 + 1506 * q^55 + 288 * q^56 + 1104 * q^57 + 324 * q^58 + 1566 * q^59 + 252 * q^60 + 1336 * q^61 + 588 * q^62 - 168 * q^63 - 112 * q^64 - 246 * q^65 - 840 * q^66 + 690 * q^67 - 480 * q^68 - 1998 * q^69 + 396 * q^70 - 1968 * q^71 - 96 * q^72 + 20 * q^73 - 984 * q^74 - 3708 * q^75 + 584 * q^76 - 954 * q^77 - 1392 * q^78 - 126 * q^79 - 48 * q^80 - 300 * q^81 + 252 * q^82 - 1554 * q^83 - 744 * q^85 - 1020 * q^86 - 990 * q^87 - 600 * q^88 - 3228 * q^89 - 1344 * q^90 - 1328 * q^91 - 876 * q^92 - 1146 * q^93 - 1572 * q^94 - 1824 * q^95 - 144 * q^96 - 1426 * q^97 - 744 * q^98 - 66 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(882))\)

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
882.3.b	\(\chi_{882}(197, \cdot)\)	882.3.b.a	2	1
		882.3.b.b	2
		882.3.b.c	2
		882.3.b.d	2
		882.3.b.e	2
		882.3.b.f	4
		882.3.b.g	4
		882.3.b.h	4
		882.3.b.i	4
882.3.c	\(\chi_{882}(685, \cdot)\)	882.3.c.a	4	1
		882.3.c.b	4
		882.3.c.c	4
		882.3.c.d	4
		882.3.c.e	4
		882.3.c.f	4
		882.3.c.g	8
882.3.i	\(\chi_{882}(569, \cdot)\)	n/a	160	2
882.3.j	\(\chi_{882}(31, \cdot)\)	n/a	160	2
882.3.n	\(\chi_{882}(19, \cdot)\)	882.3.n.a	4	2
		882.3.n.b	4
		882.3.n.c	4
		882.3.n.d	4
		882.3.n.e	4
		882.3.n.f	8
		882.3.n.g	8
		882.3.n.h	8
		882.3.n.i	8
		882.3.n.j	8
		882.3.n.k	8
882.3.o	\(\chi_{882}(97, \cdot)\)	n/a	160	2
882.3.p	\(\chi_{882}(607, \cdot)\)	n/a	160	2
882.3.q	\(\chi_{882}(491, \cdot)\)	n/a	164	2
882.3.r	\(\chi_{882}(263, \cdot)\)	n/a	160	2
882.3.s	\(\chi_{882}(557, \cdot)\)	882.3.s.a	4	2
		882.3.s.b	4
		882.3.s.c	4
		882.3.s.d	4
		882.3.s.e	8
		882.3.s.f	8
		882.3.s.g	8
		882.3.s.h	8
		882.3.s.i	8
882.3.w	\(\chi_{882}(55, \cdot)\)	n/a	288	6
882.3.x	\(\chi_{882}(71, \cdot)\)	n/a	240	6
882.3.bd	\(\chi_{882}(53, \cdot)\)	n/a	432	12
882.3.be	\(\chi_{882}(11, \cdot)\)	n/a	1344	12
882.3.bf	\(\chi_{882}(29, \cdot)\)	n/a	1344	12
882.3.bg	\(\chi_{882}(103, \cdot)\)	n/a	1344	12
882.3.bh	\(\chi_{882}(13, \cdot)\)	n/a	1344	12
882.3.bi	\(\chi_{882}(73, \cdot)\)	n/a	552	12
882.3.bm	\(\chi_{882}(61, \cdot)\)	n/a	1344	12
882.3.bn	\(\chi_{882}(65, \cdot)\)	n/a	1344	12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(882))\) into lower level spaces

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