Space of modular forms of level 2420 and weight 2

• Label: 2420.2
• Level: 2420
• Weight: 2
• Dimension: 90793
• Nonzero newspaces: 24
• Sturm bound: 696960
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(696960\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2420))\).

	Total	New	Old
Modular forms	177440	92481	84959
Cusp forms	171041	90793	80248
Eisenstein series	6399	1688	4711

Trace form

90793 * q - 92 * q^2 - 2 * q^3 - 90 * q^4 - 275 * q^5 - 270 * q^6 - 18 * q^7 - 86 * q^8 - 219 * q^9 - 119 * q^10 - 10 * q^11 - 170 * q^12 - 200 * q^13 - 70 * q^14 + 2 * q^15 - 198 * q^16 - 160 * q^17 + 4 * q^18 + 56 * q^19 - 89 * q^20 - 424 * q^21 - 40 * q^22 + 26 * q^23 + 30 * q^24 - 243 * q^25 - 166 * q^26 + 4 * q^27 + 10 * q^28 - 194 * q^29 - 125 * q^30 - 4 * q^31 - 62 * q^32 - 220 * q^33 - 250 * q^34 - 32 * q^35 - 358 * q^36 - 72 * q^37 - 190 * q^38 + 16 * q^39 - 209 * q^40 - 490 * q^41 - 270 * q^42 + 30 * q^43 - 170 * q^44 - 285 * q^45 - 370 * q^46 + 94 * q^47 - 310 * q^48 + 37 * q^49 - 219 * q^50 + 192 * q^51 - 114 * q^52 + 132 * q^53 - 110 * q^54 + 90 * q^55 - 390 * q^56 + 128 * q^57 + 58 * q^58 + 212 * q^59 - 45 * q^60 - 374 * q^61 + 210 * q^62 + 202 * q^63 + 150 * q^64 - 110 * q^65 - 170 * q^66 + 182 * q^67 + 158 * q^68 + 28 * q^69 - 85 * q^70 + 68 * q^71 + 98 * q^72 - 220 * q^73 + 90 * q^74 - 62 * q^75 - 250 * q^76 - 170 * q^77 - 210 * q^78 + 28 * q^79 - 149 * q^80 - 749 * q^81 - 194 * q^82 - 94 * q^83 - 270 * q^84 - 412 * q^85 - 470 * q^86 - 212 * q^87 - 260 * q^88 - 526 * q^89 - 579 * q^90 - 216 * q^91 - 270 * q^92 - 532 * q^93 - 470 * q^94 - 206 * q^95 - 810 * q^96 - 432 * q^97 - 496 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2420))\)

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
2420.2.a	\(\chi_{2420}(1, \cdot)\)	2420.2.a.a	1	1
		2420.2.a.b	1
		2420.2.a.c	1
		2420.2.a.d	1
		2420.2.a.e	1
		2420.2.a.f	1
		2420.2.a.g	1
		2420.2.a.h	2
		2420.2.a.i	3
		2420.2.a.j	3
		2420.2.a.k	4
		2420.2.a.l	4
		2420.2.a.m	4
		2420.2.a.n	4
		2420.2.a.o	6
2420.2.b	\(\chi_{2420}(969, \cdot)\)	2420.2.b.a	2	1
		2420.2.b.b	4
		2420.2.b.c	4
		2420.2.b.d	4
		2420.2.b.e	4
		2420.2.b.f	6
		2420.2.b.g	6
		2420.2.b.h	12
		2420.2.b.i	12
2420.2.d	\(\chi_{2420}(1451, \cdot)\)	n/a	216	1
2420.2.g	\(\chi_{2420}(2419, \cdot)\)	n/a	308	1
2420.2.k	\(\chi_{2420}(1693, \cdot)\)	n/a	108	2
2420.2.l	\(\chi_{2420}(243, \cdot)\)	n/a	618	2
2420.2.m	\(\chi_{2420}(81, \cdot)\)	n/a	144	4
2420.2.o	\(\chi_{2420}(239, \cdot)\)	n/a	1232	4
2420.2.r	\(\chi_{2420}(1371, \cdot)\)	n/a	864	4
2420.2.t	\(\chi_{2420}(9, \cdot)\)	n/a	216	4
2420.2.u	\(\chi_{2420}(221, \cdot)\)	n/a	440	10
2420.2.v	\(\chi_{2420}(233, \cdot)\)	n/a	432	8
2420.2.w	\(\chi_{2420}(3, \cdot)\)	n/a	2464	8
2420.2.ba	\(\chi_{2420}(131, \cdot)\)	n/a	2640	10
2420.2.bc	\(\chi_{2420}(89, \cdot)\)	n/a	660	10
2420.2.be	\(\chi_{2420}(219, \cdot)\)	n/a	3920	10
2420.2.bg	\(\chi_{2420}(23, \cdot)\)	n/a	7840	20
2420.2.bh	\(\chi_{2420}(153, \cdot)\)	n/a	1320	20
2420.2.bk	\(\chi_{2420}(141, \cdot)\)	n/a	1760	40
2420.2.bm	\(\chi_{2420}(19, \cdot)\)	n/a	15680	40
2420.2.bo	\(\chi_{2420}(49, \cdot)\)	n/a	2640	40
2420.2.bq	\(\chi_{2420}(51, \cdot)\)	n/a	10560	40
2420.2.bu	\(\chi_{2420}(47, \cdot)\)	n/a	31360	80
2420.2.bv	\(\chi_{2420}(13, \cdot)\)	n/a	5280	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2420))\) into lower level spaces

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