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}$