Space of modular forms of level 2420 and weight 3

• Label: 2420.3
• Level: 2420
• Weight: 3
• Dimension: 182430
• Nonzero newspaces: 24
• Sturm bound: 1045440
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1045440\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2420))\).

	Total	New	Old
Modular forms	351680	184114	167566
Cusp forms	345280	182430	162850
Eisenstein series	6400	1684	4716

Trace form

182430 * q - 92 * q^2 + 2 * q^3 - 94 * q^4 - 280 * q^5 - 286 * q^6 + 46 * q^7 - 98 * q^8 - 148 * q^9 - 139 * q^10 - 10 * q^11 - 130 * q^12 - 238 * q^13 - 174 * q^14 - 218 * q^15 - 622 * q^16 - 502 * q^17 - 368 * q^18 - 120 * q^19 - 229 * q^20 - 600 * q^21 - 40 * q^22 + 214 * q^23 + 126 * q^24 + 72 * q^25 + 122 * q^26 + 692 * q^27 + 570 * q^28 + 352 * q^29 + 355 * q^30 + 412 * q^31 + 458 * q^32 - 550 * q^33 + 706 * q^34 - 212 * q^35 + 1122 * q^36 - 1258 * q^37 + 490 * q^38 - 740 * q^39 + 51 * q^40 - 1372 * q^41 - 70 * q^42 - 910 * q^43 - 170 * q^44 - 1390 * q^45 - 746 * q^46 - 338 * q^47 - 1190 * q^48 - 128 * q^49 - 539 * q^50 + 124 * q^51 - 1974 * q^52 + 210 * q^53 - 3478 * q^54 - 20 * q^55 - 3206 * q^56 - 396 * q^57 - 1546 * q^58 - 540 * q^59 - 1045 * q^60 + 140 * q^61 - 1070 * q^62 + 1458 * q^63 - 394 * q^64 + 1280 * q^65 - 170 * q^66 + 1446 * q^67 + 554 * q^68 + 2592 * q^69 + 875 * q^70 + 1556 * q^71 + 3438 * q^72 + 1562 * q^73 + 3526 * q^74 + 218 * q^75 + 3230 * q^76 + 930 * q^77 + 4510 * q^78 + 940 * q^79 + 1691 * q^80 + 614 * q^81 + 2386 * q^82 + 714 * q^83 + 1962 * q^84 - 202 * q^85 + 194 * q^86 - 16 * q^87 - 260 * q^88 - 568 * q^89 + 1661 * q^90 + 408 * q^91 + 1010 * q^92 + 312 * q^93 + 226 * q^94 + 1794 * q^95 + 1494 * q^96 + 562 * q^97 - 8 * q^98 + 920 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2420))\)

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
2420.3.c	\(\chi_{2420}(1211, \cdot)\)	n/a	436	1
2420.3.e	\(\chi_{2420}(1209, \cdot)\)	n/a	108	1
2420.3.f	\(\chi_{2420}(241, \cdot)\)	2420.3.f.a	16	1
		2420.3.f.b	16
		2420.3.f.c	16
		2420.3.f.d	24
2420.3.h	\(\chi_{2420}(2179, \cdot)\)	n/a	636	1
2420.3.i	\(\chi_{2420}(483, \cdot)\)	n/a	1264	2
2420.3.j	\(\chi_{2420}(1453, \cdot)\)	n/a	218	2
2420.3.n	\(\chi_{2420}(1219, \cdot)\)	n/a	2528	4
2420.3.p	\(\chi_{2420}(161, \cdot)\)	n/a	288	4
2420.3.q	\(\chi_{2420}(1129, \cdot)\)	n/a	432	4
2420.3.s	\(\chi_{2420}(251, \cdot)\)	n/a	1728	4
2420.3.x	\(\chi_{2420}(403, \cdot)\)	n/a	5056	8
2420.3.y	\(\chi_{2420}(493, \cdot)\)	n/a	864	8
2420.3.z	\(\chi_{2420}(109, \cdot)\)	n/a	1320	10
2420.3.bb	\(\chi_{2420}(111, \cdot)\)	n/a	5280	10
2420.3.bd	\(\chi_{2420}(199, \cdot)\)	n/a	7880	10
2420.3.bf	\(\chi_{2420}(21, \cdot)\)	n/a	880	10
2420.3.bi	\(\chi_{2420}(133, \cdot)\)	n/a	2640	20
2420.3.bj	\(\chi_{2420}(43, \cdot)\)	n/a	15760	20
2420.3.bl	\(\chi_{2420}(41, \cdot)\)	n/a	3520	40
2420.3.bn	\(\chi_{2420}(59, \cdot)\)	n/a	31520	40
2420.3.bp	\(\chi_{2420}(31, \cdot)\)	n/a	21120	40
2420.3.br	\(\chi_{2420}(29, \cdot)\)	n/a	5280	40
2420.3.bs	\(\chi_{2420}(37, \cdot)\)	n/a	10560	80
2420.3.bt	\(\chi_{2420}(7, \cdot)\)	n/a	63040	80

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2420))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2420)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2420))\)\(^{\oplus 1}\)