Space of modular forms of level 2940 and weight 2

• Label: 2940.2
• Level: 2940
• Weight: 2
• Dimension: 86314
• Nonzero newspaces: 48
• Sturm bound: 903168
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(903168\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2940))\).

	Total	New	Old
Modular forms	230592	87474	143118
Cusp forms	220993	86314	134679
Eisenstein series	9599	1160	8439

Trace form

86314 * q + 6 * q^3 - 68 * q^4 + 14 * q^5 - 110 * q^6 + 16 * q^7 - 36 * q^8 - 90 * q^9 - 146 * q^10 - 32 * q^11 - 94 * q^12 - 232 * q^13 - 48 * q^14 - 50 * q^15 - 276 * q^16 - 68 * q^17 - 74 * q^18 - 64 * q^19 + 20 * q^20 - 274 * q^21 - 4 * q^22 - 48 * q^23 + 30 * q^24 - 302 * q^25 + 136 * q^26 - 66 * q^27 + 24 * q^28 - 228 * q^29 + 57 * q^30 - 88 * q^31 + 140 * q^32 - 132 * q^33 + 132 * q^34 - 66 * q^35 - 18 * q^36 - 384 * q^37 + 88 * q^38 - 66 * q^39 - 14 * q^40 - 172 * q^41 + 66 * q^42 - 116 * q^43 + 96 * q^44 - 116 * q^45 - 84 * q^46 - 144 * q^47 + 220 * q^48 - 420 * q^49 + 8 * q^50 - 96 * q^51 + 212 * q^52 - 68 * q^53 + 118 * q^54 - 122 * q^55 + 132 * q^56 - 68 * q^57 + 292 * q^58 - 32 * q^59 + 161 * q^60 - 416 * q^61 + 376 * q^62 - 24 * q^63 + 292 * q^64 + 296 * q^65 + 74 * q^66 + 140 * q^67 + 368 * q^68 + 188 * q^69 + 186 * q^70 + 192 * q^71 + 18 * q^72 + 128 * q^73 + 264 * q^74 + 204 * q^75 + 116 * q^76 + 144 * q^77 + 10 * q^78 + 360 * q^79 + 418 * q^80 + 330 * q^81 + 584 * q^82 + 480 * q^83 + 300 * q^84 + 68 * q^85 + 580 * q^86 + 524 * q^87 + 896 * q^88 + 404 * q^89 + 180 * q^90 + 376 * q^91 + 308 * q^92 + 680 * q^93 + 728 * q^94 + 300 * q^95 + 436 * q^96 + 624 * q^97 + 1092 * q^98 + 320 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2940))\)

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
2940.2.a	\(\chi_{2940}(1, \cdot)\)	2940.2.a.a	1	1
		2940.2.a.b	1
		2940.2.a.c	1
		2940.2.a.d	1
		2940.2.a.e	1
		2940.2.a.f	1
		2940.2.a.g	1
		2940.2.a.h	1
		2940.2.a.i	1
		2940.2.a.j	1
		2940.2.a.k	1
		2940.2.a.l	1
		2940.2.a.m	2
		2940.2.a.n	2
		2940.2.a.o	2
		2940.2.a.p	2
		2940.2.a.q	2
		2940.2.a.r	2
		2940.2.a.s	2
		2940.2.a.t	2
2940.2.c	\(\chi_{2940}(391, \cdot)\)	n/a	160	1
2940.2.d	\(\chi_{2940}(881, \cdot)\)	2940.2.d.a	10	1
		2940.2.d.b	10
		2940.2.d.c	16
		2940.2.d.d	16
2940.2.f	\(\chi_{2940}(1469, \cdot)\)	2940.2.f.a	32	1
		2940.2.f.b	48
2940.2.i	\(\chi_{2940}(979, \cdot)\)	n/a	240	1
2940.2.k	\(\chi_{2940}(589, \cdot)\)	2940.2.k.a	2	1
		2940.2.k.b	2
		2940.2.k.c	2
		2940.2.k.d	2
		2940.2.k.e	2
		2940.2.k.f	8
		2940.2.k.g	8
		2940.2.k.h	16
2940.2.l	\(\chi_{2940}(1079, \cdot)\)	n/a	472	1
2940.2.n	\(\chi_{2940}(491, \cdot)\)	n/a	328	1
2940.2.q	\(\chi_{2940}(361, \cdot)\)	2940.2.q.a	2	2
		2940.2.q.b	2
		2940.2.q.c	2
		2940.2.q.d	2
		2940.2.q.e	2
		2940.2.q.f	2
		2940.2.q.g	2
		2940.2.q.h	2
		2940.2.q.i	2
		2940.2.q.j	2
		2940.2.q.k	2
		2940.2.q.l	2
		2940.2.q.m	2
		2940.2.q.n	2
		2940.2.q.o	4
		2940.2.q.p	4
		2940.2.q.q	4
		2940.2.q.r	4
		2940.2.q.s	4
		2940.2.q.t	4
2940.2.s	\(\chi_{2940}(197, \cdot)\)	n/a	164	2
2940.2.t	\(\chi_{2940}(883, \cdot)\)	n/a	492	2
2940.2.w	\(\chi_{2940}(587, \cdot)\)	n/a	928	2
2940.2.x	\(\chi_{2940}(97, \cdot)\)	2940.2.x.a	24	2
		2940.2.x.b	24
		2940.2.x.c	32
2940.2.ba	\(\chi_{2940}(1439, \cdot)\)	n/a	928	2
2940.2.bb	\(\chi_{2940}(949, \cdot)\)	2940.2.bb.a	4	2
		2940.2.bb.b	4
		2940.2.bb.c	4
		2940.2.bb.d	4
		2940.2.bb.e	4
		2940.2.bb.f	4
		2940.2.bb.g	4
		2940.2.bb.h	4
		2940.2.bb.i	16
		2940.2.bb.j	32
2940.2.bf	\(\chi_{2940}(851, \cdot)\)	n/a	640	2
2940.2.bh	\(\chi_{2940}(521, \cdot)\)	n/a	108	2
2940.2.bi	\(\chi_{2940}(31, \cdot)\)	n/a	320	2
2940.2.bk	\(\chi_{2940}(19, \cdot)\)	n/a	480	2
2940.2.bn	\(\chi_{2940}(509, \cdot)\)	n/a	160	2
2940.2.bo	\(\chi_{2940}(421, \cdot)\)	n/a	216	6
2940.2.bp	\(\chi_{2940}(313, \cdot)\)	n/a	160	4
2940.2.bs	\(\chi_{2940}(227, \cdot)\)	n/a	1856	4
2940.2.bt	\(\chi_{2940}(67, \cdot)\)	n/a	960	4
2940.2.bw	\(\chi_{2940}(557, \cdot)\)	n/a	320	4
2940.2.by	\(\chi_{2940}(71, \cdot)\)	n/a	2688	6
2940.2.ca	\(\chi_{2940}(239, \cdot)\)	n/a	3984	6
2940.2.cd	\(\chi_{2940}(169, \cdot)\)	n/a	336	6
2940.2.cf	\(\chi_{2940}(139, \cdot)\)	n/a	2016	6
2940.2.cg	\(\chi_{2940}(209, \cdot)\)	n/a	672	6
2940.2.ci	\(\chi_{2940}(41, \cdot)\)	n/a	456	6
2940.2.cl	\(\chi_{2940}(811, \cdot)\)	n/a	1344	6
2940.2.cm	\(\chi_{2940}(121, \cdot)\)	n/a	456	12
2940.2.cn	\(\chi_{2940}(83, \cdot)\)	n/a	7968	12
2940.2.cq	\(\chi_{2940}(13, \cdot)\)	n/a	672	12
2940.2.cr	\(\chi_{2940}(113, \cdot)\)	n/a	1344	12
2940.2.cu	\(\chi_{2940}(43, \cdot)\)	n/a	4032	12
2940.2.cw	\(\chi_{2940}(89, \cdot)\)	n/a	1344	12
2940.2.cx	\(\chi_{2940}(199, \cdot)\)	n/a	4032	12
2940.2.cz	\(\chi_{2940}(271, \cdot)\)	n/a	2688	12
2940.2.dc	\(\chi_{2940}(101, \cdot)\)	n/a	888	12
2940.2.de	\(\chi_{2940}(11, \cdot)\)	n/a	5376	12
2940.2.dg	\(\chi_{2940}(109, \cdot)\)	n/a	672	12
2940.2.dj	\(\chi_{2940}(179, \cdot)\)	n/a	7968	12
2940.2.dl	\(\chi_{2940}(163, \cdot)\)	n/a	8064	24
2940.2.dm	\(\chi_{2940}(53, \cdot)\)	n/a	2688	24
2940.2.dp	\(\chi_{2940}(73, \cdot)\)	n/a	1344	24
2940.2.dq	\(\chi_{2940}(47, \cdot)\)	n/a	15936	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2940))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2940)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 2}\)