Space of modular forms of level 2450 and weight 4

• Label: 2450.4
• Level: 2450
• Weight: 4
• Dimension: 156015
• Nonzero newspaces: 24
• Sturm bound: 1411200
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1411200\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2450))\).

	Total	New	Old
Modular forms	532560	156015	376545
Cusp forms	525840	156015	369825
Eisenstein series	6720	0	6720

Trace form

156015 * q - 4 * q^2 - 8 * q^3 + 8 * q^4 + 5 * q^5 + 88 * q^6 + 48 * q^7 - 16 * q^8 - 250 * q^9 - 50 * q^10 + 4 * q^11 - 32 * q^12 - 16 * q^13 - 132 * q^14 + 80 * q^15 - 96 * q^16 + 808 * q^17 + 638 * q^18 + 320 * q^19 - 80 * q^20 + 72 * q^21 - 336 * q^22 - 556 * q^23 - 192 * q^24 + 1373 * q^25 + 2648 * q^26 + 4264 * q^27 + 264 * q^28 - 1540 * q^29 - 1656 * q^30 - 3716 * q^31 + 96 * q^32 - 12108 * q^33 - 4838 * q^34 - 2448 * q^35 - 5736 * q^36 - 2841 * q^37 - 1436 * q^38 - 492 * q^39 + 120 * q^40 + 4160 * q^41 + 2340 * q^42 + 6472 * q^43 + 3320 * q^44 + 8669 * q^45 + 4388 * q^46 + 6572 * q^47 - 224 * q^48 - 7974 * q^49 + 350 * q^50 - 10576 * q^51 - 664 * q^52 - 7065 * q^53 - 2460 * q^54 + 5668 * q^55 + 288 * q^56 + 17056 * q^57 + 4896 * q^58 + 17648 * q^59 + 2720 * q^60 + 11776 * q^61 + 9700 * q^62 + 3936 * q^63 - 640 * q^64 - 3971 * q^65 + 1480 * q^66 - 19468 * q^67 - 1248 * q^68 - 28344 * q^69 - 12592 * q^71 + 752 * q^72 - 27184 * q^73 - 8400 * q^74 - 19528 * q^75 - 4048 * q^76 - 4098 * q^77 - 10360 * q^78 - 916 * q^79 + 80 * q^80 + 29150 * q^81 + 2280 * q^82 + 34236 * q^83 + 912 * q^84 + 23021 * q^85 + 21624 * q^86 + 87544 * q^87 + 13248 * q^88 + 68635 * q^89 + 29022 * q^90 + 9450 * q^91 + 14432 * q^92 + 4336 * q^93 + 6560 * q^94 - 7436 * q^95 - 2432 * q^96 - 31420 * q^97 - 15216 * q^98 - 69580 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2450))\)

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
2450.4.a	\(\chi_{2450}(1, \cdot)\)	2450.4.a.a	1	1
		2450.4.a.b	1
		2450.4.a.c	1
		2450.4.a.d	1
		2450.4.a.e	1
		2450.4.a.f	1
		2450.4.a.g	1
		2450.4.a.h	1
		2450.4.a.i	1
		2450.4.a.j	1
		2450.4.a.k	1
		2450.4.a.l	1
		2450.4.a.m	1
		2450.4.a.n	1
		2450.4.a.o	1
		2450.4.a.p	1
		2450.4.a.q	1
		2450.4.a.r	1
		2450.4.a.s	1
		2450.4.a.t	1
		2450.4.a.u	1
		2450.4.a.v	1
		2450.4.a.w	1
		2450.4.a.x	1
		2450.4.a.y	1
		2450.4.a.z	1
		2450.4.a.ba	1
		2450.4.a.bb	1
		2450.4.a.bc	1
		2450.4.a.bd	1
		2450.4.a.be	1
		2450.4.a.bf	1
		2450.4.a.bg	1
		2450.4.a.bh	1
		2450.4.a.bi	1
		2450.4.a.bj	1
		2450.4.a.bk	1
		2450.4.a.bl	1
		2450.4.a.bm	1
		2450.4.a.bn	1
		2450.4.a.bo	1
		2450.4.a.bp	1
		2450.4.a.bq	1
		2450.4.a.br	2
		2450.4.a.bs	2
		2450.4.a.bt	2
		2450.4.a.bu	2
		2450.4.a.bv	2
		2450.4.a.bw	2
		2450.4.a.bx	2
		2450.4.a.by	2
		2450.4.a.bz	2
		2450.4.a.ca	2
		2450.4.a.cb	3
		2450.4.a.cc	3
		2450.4.a.cd	3
		2450.4.a.ce	3
		2450.4.a.cf	3
		2450.4.a.cg	3
		2450.4.a.ch	3
		2450.4.a.ci	3
		2450.4.a.cj	4
		2450.4.a.ck	4
		2450.4.a.cl	4
2450.4.a.cm	4
2450.4.a.cn	4
2450.4.a.co	4
2450.4.a.cp	4
2450.4.a.cq	4
2450.4.a.cr	4
2450.4.a.cs	4
2450.4.a.ct	4
2450.4.a.cu	4
2450.4.a.cv	6
2450.4.a.cw	6
2450.4.a.cx	6
2450.4.a.cy	6
2450.4.a.cz	8
2450.4.a.da	8
2450.4.a.db	10
2450.4.a.dc	10
2450.4.c	\(\chi_{2450}(99, \cdot)\)	n/a	184	1
2450.4.e	\(\chi_{2450}(851, \cdot)\)	n/a	380	2
2450.4.g	\(\chi_{2450}(293, \cdot)\)	n/a	360	2
2450.4.h	\(\chi_{2450}(491, \cdot)\)	n/a	1228	4
2450.4.j	\(\chi_{2450}(949, \cdot)\)	n/a	360	2
2450.4.l	\(\chi_{2450}(351, \cdot)\)	n/a	1596	6
2450.4.n	\(\chi_{2450}(589, \cdot)\)	n/a	1232	4
2450.4.p	\(\chi_{2450}(607, \cdot)\)	n/a	720	4
2450.4.t	\(\chi_{2450}(449, \cdot)\)	n/a	1512	6
2450.4.u	\(\chi_{2450}(361, \cdot)\)	n/a	2400	8
2450.4.v	\(\chi_{2450}(97, \cdot)\)	n/a	2400	8
2450.4.x	\(\chi_{2450}(51, \cdot)\)	n/a	3192	12
2450.4.z	\(\chi_{2450}(307, \cdot)\)	n/a	3024	12
2450.4.bb	\(\chi_{2450}(79, \cdot)\)	n/a	2400	8
2450.4.bd	\(\chi_{2450}(71, \cdot)\)	n/a	10080	24
2450.4.be	\(\chi_{2450}(149, \cdot)\)	n/a	3024	12
2450.4.bi	\(\chi_{2450}(117, \cdot)\)	n/a	4800	16
2450.4.bj	\(\chi_{2450}(29, \cdot)\)	n/a	10080	24
2450.4.bm	\(\chi_{2450}(143, \cdot)\)	n/a	6048	24
2450.4.bo	\(\chi_{2450}(11, \cdot)\)	n/a	20160	48
2450.4.bp	\(\chi_{2450}(13, \cdot)\)	n/a	20160	48
2450.4.bt	\(\chi_{2450}(9, \cdot)\)	n/a	20160	48
2450.4.bv	\(\chi_{2450}(3, \cdot)\)	n/a	40320	96

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2450))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2450)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 2}\)