Space of modular forms of level 980 and weight 3

• Label: 980.3
• Level: 980
• Weight: 3
• Dimension: 28674
• Nonzero newspaces: 24
• Sturm bound: 169344
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(169344\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(980))\).

	Total	New	Old
Modular forms	57648	29254	28394
Cusp forms	55248	28674	26574
Eisenstein series	2400	580	1820

Trace form

28674 * q - 32 * q^2 + 14 * q^3 - 34 * q^4 - 94 * q^5 - 118 * q^6 - 8 * q^7 - 122 * q^8 - 212 * q^9 - 93 * q^10 - 88 * q^11 - 50 * q^12 - 82 * q^13 - 12 * q^14 + 110 * q^15 + 102 * q^16 + 122 * q^17 + 400 * q^18 + 108 * q^19 + 157 * q^20 - 306 * q^21 + 274 * q^22 - 250 * q^23 + 150 * q^24 - 302 * q^25 - 186 * q^26 - 472 * q^27 - 84 * q^28 - 220 * q^29 - 275 * q^30 - 256 * q^31 - 742 * q^32 + 28 * q^33 - 870 * q^34 - 33 * q^35 - 1210 * q^36 + 58 * q^37 - 706 * q^38 - 378 * q^39 - 279 * q^40 - 508 * q^41 + 246 * q^42 + 142 * q^43 + 814 * q^44 + 479 * q^45 + 914 * q^46 + 450 * q^47 + 1680 * q^48 + 440 * q^49 + 542 * q^50 + 1480 * q^51 + 1334 * q^52 + 1214 * q^53 + 1510 * q^54 + 1347 * q^55 + 456 * q^56 + 848 * q^57 + 690 * q^58 + 1320 * q^59 + 1345 * q^60 + 1534 * q^61 - 122 * q^62 + 1200 * q^63 - 154 * q^64 + 244 * q^65 - 358 * q^66 + 6 * q^67 + 86 * q^68 - 908 * q^69 - 57 * q^70 - 668 * q^71 + 42 * q^72 - 2086 * q^73 + 618 * q^74 - 1496 * q^75 - 102 * q^76 - 846 * q^77 - 158 * q^78 - 1036 * q^79 - 864 * q^80 + 186 * q^81 + 872 * q^82 + 882 * q^83 + 4284 * q^84 - 1076 * q^85 + 1028 * q^86 + 1184 * q^87 + 1612 * q^88 + 792 * q^89 + 600 * q^90 + 480 * q^91 - 888 * q^92 + 1420 * q^93 + 316 * q^94 - 794 * q^95 - 220 * q^96 + 2826 * q^97 - 984 * q^98 - 192 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(980))\)

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
980.3.b	\(\chi_{980}(491, \cdot)\)	n/a	164	1
980.3.d	\(\chi_{980}(881, \cdot)\)	980.3.d.a	12	1
		980.3.d.b	16
980.3.f	\(\chi_{980}(99, \cdot)\)	n/a	236	1
980.3.h	\(\chi_{980}(489, \cdot)\)	980.3.h.a	16	1
		980.3.h.b	24
980.3.j	\(\chi_{980}(587, \cdot)\)	n/a	464	2
980.3.l	\(\chi_{980}(197, \cdot)\)	980.3.l.a	2	2
		980.3.l.b	4
		980.3.l.c	8
		980.3.l.d	12
		980.3.l.e	16
		980.3.l.f	16
		980.3.l.g	24
980.3.n	\(\chi_{980}(129, \cdot)\)	980.3.n.a	4	2
		980.3.n.b	4
		980.3.n.c	8
		980.3.n.d	16
		980.3.n.e	48
980.3.p	\(\chi_{980}(79, \cdot)\)	n/a	464	2
980.3.r	\(\chi_{980}(521, \cdot)\)	980.3.r.a	8	2
		980.3.r.b	12
		980.3.r.c	32
980.3.t	\(\chi_{980}(471, \cdot)\)	n/a	320	2
980.3.w	\(\chi_{980}(177, \cdot)\)	n/a	160	4
980.3.y	\(\chi_{980}(227, \cdot)\)	n/a	928	4
980.3.z	\(\chi_{980}(69, \cdot)\)	n/a	336	6
980.3.ba	\(\chi_{980}(239, \cdot)\)	n/a	1992	6
980.3.bc	\(\chi_{980}(41, \cdot)\)	n/a	216	6
980.3.be	\(\chi_{980}(71, \cdot)\)	n/a	1344	6
980.3.bh	\(\chi_{980}(57, \cdot)\)	n/a	672	12
980.3.bj	\(\chi_{980}(27, \cdot)\)	n/a	3984	12
980.3.bm	\(\chi_{980}(11, \cdot)\)	n/a	2688	12
980.3.bo	\(\chi_{980}(61, \cdot)\)	n/a	456	12
980.3.bq	\(\chi_{980}(39, \cdot)\)	n/a	3984	12
980.3.br	\(\chi_{980}(89, \cdot)\)	n/a	672	12
980.3.bt	\(\chi_{980}(3, \cdot)\)	n/a	7968	24
980.3.bv	\(\chi_{980}(37, \cdot)\)	n/a	1344	24

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(980))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(980)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)