Space of modular forms of level 2420 and weight 4

• Label: 2420.4
• Level: 2420
• Weight: 4
• Dimension: 274067
• Nonzero newspaces: 24
• Sturm bound: 1393920
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1393920\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2420))\).

	Total	New	Old
Modular forms	525920	275755	250165
Cusp forms	519520	274067	245453
Eisenstein series	6400	1688	4712

Trace form

274067 * q - 92 * q^2 + 4 * q^3 - 90 * q^4 - 255 * q^5 - 262 * q^6 - 56 * q^7 - 134 * q^8 + 31 * q^9 - 199 * q^10 + 100 * q^11 - 250 * q^12 + 28 * q^13 + 610 * q^14 + 392 * q^15 + 634 * q^16 - 976 * q^17 - 684 * q^18 - 1024 * q^19 - 769 * q^20 - 2236 * q^21 - 1360 * q^22 - 1872 * q^23 - 1890 * q^24 - 1033 * q^25 - 830 * q^26 + 508 * q^27 + 1130 * q^28 + 2246 * q^29 + 395 * q^30 + 3688 * q^31 - 702 * q^32 + 3410 * q^33 - 3930 * q^34 + 1648 * q^35 - 918 * q^36 + 720 * q^37 + 2810 * q^38 - 1184 * q^39 + 3871 * q^40 - 6374 * q^41 + 10250 * q^42 - 1820 * q^43 + 2910 * q^44 - 4405 * q^45 + 3638 * q^46 - 952 * q^47 + 2250 * q^48 - 3693 * q^49 - 2279 * q^50 - 564 * q^51 + 4846 * q^52 + 10304 * q^53 - 110 * q^54 - 1450 * q^55 - 2502 * q^56 + 4656 * q^57 - 2158 * q^58 - 5568 * q^59 - 3005 * q^60 - 9906 * q^61 - 13550 * q^62 - 13824 * q^63 - 15210 * q^64 - 4350 * q^65 - 8750 * q^66 - 5556 * q^67 - 17858 * q^68 - 212 * q^69 - 12005 * q^70 - 936 * q^71 - 24462 * q^72 + 468 * q^73 - 7630 * q^74 + 8648 * q^75 + 550 * q^76 + 6980 * q^77 + 21030 * q^78 + 13928 * q^79 + 16971 * q^80 + 21717 * q^81 + 28406 * q^82 - 712 * q^83 + 23490 * q^84 + 2518 * q^85 + 10618 * q^86 - 7544 * q^87 + 13820 * q^88 - 3406 * q^89 - 11279 * q^90 - 14608 * q^91 - 9630 * q^92 - 22716 * q^93 - 7630 * q^94 - 8856 * q^95 - 17162 * q^96 - 3160 * q^97 - 9864 * q^98 + 7740 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2420))\)

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
2420.4.a	\(\chi_{2420}(1, \cdot)\)	2420.4.a.a	1	1
		2420.4.a.b	1
		2420.4.a.c	1
		2420.4.a.d	1
		2420.4.a.e	1
		2420.4.a.f	1
		2420.4.a.g	2
		2420.4.a.h	2
		2420.4.a.i	3
		2420.4.a.j	3
		2420.4.a.k	3
		2420.4.a.l	4
		2420.4.a.m	6
		2420.4.a.n	6
		2420.4.a.o	6
		2420.4.a.p	8
		2420.4.a.q	12
		2420.4.a.r	12
		2420.4.a.s	12
		2420.4.a.t	12
		2420.4.a.u	12
2420.4.b	\(\chi_{2420}(969, \cdot)\)	n/a	164	1
2420.4.d	\(\chi_{2420}(1451, \cdot)\)	n/a	648	1
2420.4.g	\(\chi_{2420}(2419, \cdot)\)	n/a	956	1
2420.4.k	\(\chi_{2420}(1693, \cdot)\)	n/a	324	2
2420.4.l	\(\chi_{2420}(243, \cdot)\)	n/a	1926	2
2420.4.m	\(\chi_{2420}(81, \cdot)\)	n/a	432	4
2420.4.o	\(\chi_{2420}(239, \cdot)\)	n/a	3824	4
2420.4.r	\(\chi_{2420}(1371, \cdot)\)	n/a	2592	4
2420.4.t	\(\chi_{2420}(9, \cdot)\)	n/a	648	4
2420.4.u	\(\chi_{2420}(221, \cdot)\)	n/a	1320	10
2420.4.v	\(\chi_{2420}(233, \cdot)\)	n/a	1296	8
2420.4.w	\(\chi_{2420}(3, \cdot)\)	n/a	7648	8
2420.4.ba	\(\chi_{2420}(131, \cdot)\)	n/a	7920	10
2420.4.bc	\(\chi_{2420}(89, \cdot)\)	n/a	1980	10
2420.4.be	\(\chi_{2420}(219, \cdot)\)	n/a	11840	10
2420.4.bg	\(\chi_{2420}(23, \cdot)\)	n/a	23680	20
2420.4.bh	\(\chi_{2420}(153, \cdot)\)	n/a	3960	20
2420.4.bk	\(\chi_{2420}(141, \cdot)\)	n/a	5280	40
2420.4.bm	\(\chi_{2420}(19, \cdot)\)	n/a	47360	40
2420.4.bo	\(\chi_{2420}(49, \cdot)\)	n/a	7920	40
2420.4.bq	\(\chi_{2420}(51, \cdot)\)	n/a	31680	40
2420.4.bu	\(\chi_{2420}(47, \cdot)\)	n/a	94720	80
2420.4.bv	\(\chi_{2420}(13, \cdot)\)	n/a	15840	80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2420))\) into lower level spaces

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